Wickedly Tough Reasoning Brainteasers

Seemingly Tough Yet Simple Puzzles on Logical Reasoning, a la Poirot!

Hercule Poirot was a wildly popular character created by Agatha Christie, who believed in solving problems by working systematically to eliminate possibilities and arrive at a final conclusion. Where Holmes excelled at solving problems by establishing abstract relationships based on limited or disjointed information, Poirot was in a league of his own in working methodically and step-by-step, taking his time to work out his conclusions.

In today’s world of instant gratification and instant reactions, it is becoming extremely difficult for us to hold a train of thought for any length of time. Logical thought is getting increasingly beyond the grasp of people, fully evidenced in the mindless exchanges we witness so often on social media platforms as well as the lack of thought behind instant forwards on various messaging platforms.

Is the current generation more intelligent, or is it merely -and perhaps dangerously- over-dependent on use of technology to find answers? Would you like to find out if you are left with sufficient capacity to reason things out in a logical and systematic manner?

Put on your thinking caps, then, and let’s go. Don’t forget to have pen and paper ready, as you may be required to jot down your thoughts in most such puzzles.

Be forewarned: Some of these will be the toughest puzzles you are likely to encounter anywhere, and will really test your fortitude!

We start with a few simple ones, just to keep morale high :))

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5.1    Who is the tallest and who is the shortest?

Amar is taller than Rohan, but shorter than Krish. Amy is shorter than Rohan, but taller than Sheena. Krish is shorter than Ram.

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5.2    Dudeney was a master puzzler, and we have already seen a few of his puzzles earlier on. Reproduced below is another of his classic mind-bogglers, published in Strand magazine in 1929.

Arrange all the 10 digits in three arithmetical sums, employing three of the four operations of addition, subtraction, multiplication, and division, and using no signs except the ordinary ones implying those operations

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5.3    You are in a room which has three switches. You cannot see or hear anything outside, and there is only one closed door through which you may exit the room. Once past the door, you cannot touch it again.

Each switch controls one lightbulb in the corridor outside the room. You cannot see the bulbs or the light from inside.

You have to identify which switch controls which bulb. How do you do it?

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5.4    There are Eighteen boys in a class, along with some girls. Thirteen of the kids wear a Yellow shirt, but three of the kids neither wear a yellow shirt nor are boys. If eight boys wear a white shirt, how many kids are there in total?

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5.5    Four playing cards are placed face down on the table. Each card is of a different suit and each has a different face value: a Three, a Four, a Five and a Six.

Some information about them is given below, the task is to find out each card’s suit, face value and position basis this.

  1. The sum of the two cards in the middle is an even number.
  2. The Club is not in the middle.
  3. The Four has black suits on either side of it
  4. The Club lies to the right of the Three but is not placed next to it
  5. The Spade lies to the left of the Heart

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5.6    Sometimes, the way a puzzle is presented makes it difficult for us to comprehend it. The key, of course, is to fix a starting point and then fit in the facts provided to find the solution. Try your hand at the one below:

What day would tomorrow be if Sunday was five days after the day before yesterday?

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5.7    Seated in the Club lounge are, X, Y and Z. Their professions, in random order, are: Doctor, Engineer and Businessman. In the same lounge there are three Lawyers, who are Mr X, Mr. Y and Mr. Z. They each stay in one of three places: Delhi, Shimla or a town exactly midway between them.

Given the clues below, can you establish the identities of X,Y and Z?

  1. The lawyer with the same name as the Engineer lives in Delhi
  2. Mr. Z earns Rs. 16 lakh in a year
  3. Mr Y is a resident of Shimla
  4. The Engineer lives exactly midway between Delhi and Shimla
  5. The Engineer’s nearest neighbour is a lawyer who earns exactly three times as much as the Engineer
  6. The Doctor was beaten by X in a game of Chess

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5.8    If all Bings are Bongs and some Bungs are Bings, which of the below statements is definitely true?

(i) All Bings are Bungs.

(ii) Some Bongs are Bungs.

(iii) Some Bings are not Bungs

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5.9    This is a very interesting problem from the Central New York Mathletics in 2011: Mrs. Barnard has three sons, Bartholemew, Barton and Benjamin.  One is an avid bowler in Baltimore, a second is in Bainbridge, and the third is in Binghampton. One is boating and another is barbequeing. Bartholemew is not in Baltimore. Benjamin is not in Bainbridge, and the son who barbeques is not in Binghampton. The bowling enthusiast is not Benjamin.

Who is barbequeing and where is he?

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5.10 Here’s another one from the Central New York Mathletics, 2010:  One rainy evening, five military men were murdered in the old mansion on Willow Lane (a General, a Captain, a Lieutenant, a Sergeant, and a Corporal). The murders took place in the bedroom, basement, pantry, den, and attic of the house. No two men were murdered in the same room or with the same weapon. The weapons used were poison, a poker, a gun, a knife, and a shovel. From the clues given, try to determine the room in which each man was killed and the weapon used to do him in.

1.       The murder with the shovel was not done in the den or the attic; neither the captain nor the lieutenant was killed with the shovel, nor was either killed in the den or the attic.

2.      The captain was not murdered in the bedroom.

3.      The poker was not the murder weapon used in the attic.

4.      Neither the general nor the corporal was murdered with poison, a gun, or a shovel.

5.      The man murdered in the basement had just had dinner with the corporal, the captain, the man done in with poison, and the victim of the poker.

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5.11 Abhi, Bob, Jill, Sonu and Amy have birthdays between Jan to May, with only one person in each month. They each like a different type of dessert on their birthday: Sweets, Chocolates, Pastries, Sundaes and Dry fruits.

The one who likes Pastries is born in the middle of all months, while the favorite of the May born is Dry fruits. Jill doesn’t like Dry fruits or Sundaes. Amy loves Sweets and is born in the month immediately after Jill’s birthday month. Sonu doesn’t like Sundaes but gifts Chocolates to Abhi in February.

Can you find out whose birthday is in which month, and what do they each like for dessert?

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5.12 Three countries A, B and C participate in a sporting event which has 10 events in total. A gold medal is worth 3 points, a silver medal is worth 2 points and a bronze medal is worth 1 point. C wins more gold medals than either A or B. The total number of medals won by C is also 1 more than B and 2 more than A. However, A finishes the event on top with overall 1 point more than B and 2 points more than C.

Can you find out which country won how many of each medal, and also the total points won by each?

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5.13 In a three-storeyed store, A, B, C, D, E and F are six staff of which three are female. There are three departments – Accounts, Administration and Personnel, on the three floors. All the females work on different floors and in different departments. Persons working in the same department are not together on the same floor, and each floor has exactly two staff.  

B and E work in the same department but not in Personnel. D is a female who works in Administration, but is not on the 2nd Floor. E and A are on the 1st and 3rd floor respectively and work in the same department. C is a male who works on the 1st floor. A total of two people work in Admin.

Can you establish the gender of each person and find out who works where?

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5.14 There are 70 people of which 30 are females.

a) 30 people are married.

b) 15 males are married of which 8 are below 30 years of age

c) 19 married people are above 30 years

d) 12 males are above 30 years of age.

e) 24 people are above 30 years of age.

Can you find out the count of males and females as per their age and marital status?          

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5.15 This puzzle is one allegedly devised by Albert Einstein, and hence also known as Einstein’s puzzle or the Zebra riddle. It is alleged that only 2% of the population can solve it. There is no conclusive evidence as to the origin of this puzzle, but it remains a favorite of puzzlers worldwide. Have a go at it, and see for yourself.

There are 5 houses in 5 different colors. All the 5 owners are of different nationality. The 5 owners drink different beverages, smoke different brand of cigars, and own different pets. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage.

• The Brit lives in the red house.
• The Spaniard owns the dog.
• Coffee is drunk in the green house.
• The Ukrainian drinks tea.
• The green house is immediately to the right of the ivory house.
• The Old Gold smoker owns snails.
• Kools are smoked in the yellow house.
• Milk is drunk in the middle house.
• The Norwegian lives in the first house.
• The man who smokes Chesterfields lives in the house next to the man with the fox.
• Kools are smoked in the house next to the house where the horse is kept.
• The Lucky Strike smoker drinks orange juice.
• The Japanese smokes Parliaments.
• The Norwegian lives next to the blue house.

Who owns the zebra? And who drinks water?

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5.16 This is what is known as a self-referential puzzle, wonderful for boosting the way of logical thought. We start with this practice problem, then you can attempt the really hard one which will follow.

Q 1) What is the answer to the second question?

A. A

B. B

C. C

D. D

Q.2) How many correct answers are option B?

A. 0

B. 1

C. 2

D. 3

Q.3) Is there a question with the correct answer A?

A. No

B. Yes,1

C. Yes, 2

D. Yes, all 3

Answers: A, A and C

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5.17 This puzzle will be a truly challenging one. Do keep a pen and paper handy, and keep filling in the options as you go along. Read all the questions fully, and try to understand which questions are dependent on each other and what should be the logical answer to them. This will give you a starting point for solving this type of puzzle.

There is only one answer to each question, and a total of 20 questions. The key to solving this is to arrange your data in a solution grid, which will keep things organized and give you a handle on the inter-relationships between the various questions and answers.

Given that the answer to Q. 20 is E. Now, find the answers to Questions 1-19.

1.      The first question whose answer is B is question:

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

2.      The only two consecutive questions with identical answers are questions:

(A) 6 and 7

(B) 7 and 8

(C) 8 and 9

(D) 9 and 10

(E) 10 and 11

3.      The number of questions with the answer E is:

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

4.      The number of questions with the answer A is:

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

5.      The answer to this question is the same as the answer to question:

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

6.      The answer to question 17 is:

(A) C

(B) D

(C) E

(D) none of the above

(E) all of the above

7.      Alphabetically, the answer to this question and the answer to the following question are:

(A) 4 apart

(B) 3 apart

(C) 2 apart

(D) 1 apart

(E) the same

8.      The number of questions whose answers are vowels is:

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

9.      The next question with the same answer as this one is question:

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14

10.    The answer to question 16 is:

(A) D

(B) A

(C) E

(D) B

(E) C

11.    The number of questions preceding this one with the answer B is:

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

12.    The number of questions whose answer is a consonant is:

(A) an even number

(B) an odd number

(C) a perfect square

(D) a prime

(E) divisible by 5

13.    The only odd-numbered problem with answer A is:

(A) 9

(B) 11

(C) 13

(D) 15

(E) 17

14.    The number of questions with answer D is

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10

15.    The answer to question 12 is:

(A) A

(B) B

(C) C

(D) D

(E) E

16.    The answer to question 10 is:

(A) D

(B) C

(C) B

(D) A

(E) E

17.    The answer to question 6 is:

(A) C

(B) D

(C) E

(D) none of the above

(E) all of the above

18.    The number of questions with answer A equals the number of questions with answer:

(A) B

(B) C

(C) D

(D) E

(E) none of the above

19.    The answer to this question is:

(A) A

(B) B

(C) C

(D) D

(E) E

20.    Standardized test is to intelligence as barometer is to:

(A) temperature (only)

(B) wind-velocity (only)

(C) latitude (only)

(D) longitude (only)

(E) temperature, wind-velocity, latitude, and longitude

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SOLUTIONS TO CHAPTER 5

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5.1      Basis the three height comparisons provided, the facts can be represented visually like this:

 So, Ram will be the tallest and Sheena will be the shortest

5.2      To form three logical equations using each digit just once, there must be two equations involving only three digits, and one equation will use 4 digits.

We see that 0 cannot be used with any operator, hence can only be used as the second digit of a two digit resultant of any operation. Thus, the equation involving 4 digits must necessarily have zero in the units place of a two digit resultant.

With zero in the units place of the resultant, the only possible candidates for the digit in the tens place of the resultant are 1,2,3 and 4 ( this is because the largest number possible with a zero in units place is 8*5=40)

Only possibilities for our first equation are:

8+2=10, 7+3=10, 6+4=10, 5*2=10, 5*4=20, 5*6=30 and 5*8=40

We can immediately see that 9 is missing here. So, 9 must be part of one of the other two equations. What are the options for an equation using 9?

We know the resultant of each equation will be > zero and in single digits. The only possibilities are given below:

9-1=8. 9-2=7, 9-3=6, 9-4=5            Or, alternatively:       8+1=9, 7+2=9, 6+3=9, 5+4=9.

Whether we take subtraction or addition, will not really matter in finalizing the options for the third equation as what concerns us is mainly the digits remaining to be used for the final equation.

So let’s see the possibilities we have after accounting for the first two equations:

The first column gives the possibilities we have for the first equation. The second column contains the available options for the second equation corresponding to the first equation, while the third column gives the possibilities of forming a third equation using the remaining digits and operators available for use in the third equation:   

Hence we can see that the only available option for Equation 1 is 5*4=20

Equation 2 may be either 9-3=6 , or 6+3=9

Accordingly, equation 3 will be either 1+7=8, or 8-1=7, depending on which operator we have selected for the second equation.

5.3      Any bulb when left on for a period of time will turn hot, even if just a little. So, all you need to do is to keep one switch in one position for 5 minutes, then switch it off. Then you switch on any one of the remaining switches, and go out of the door and check the bulbs outside. One bulb will be off and cool, second will be off but hot, and the third bulb will be on. Thus, you can immediately relate the bulb to the switch.

5.4       Think in terms of set theory and venn diagrams for such puzzles. The facts provided can be represented like this:

We have to calculate the value of ‘N’, which is the total number of kids in class. x,y,and z are also unknown.

From the figure, we get:

x= no. of boys in yellow shirt = 18-8 = 10

x+y=13, on substituting the value of x we get: y=13-10=3

Therefore, z=y+3=6

Hence, we get:  N =Total ( boys + Girls) =18+z =  24

Thus, there are 24 kids in class.

5.5      The four cards are 3,4,5 and 6. Let’s examine our conditions:

For the sum of two numbers to be even, either both numbers will be even or both numbers will be odd. Since it is mentioned that the 4 has black suits on either side, hence 4 has to be one of the cards in the middle. Thus, the second card in the middle has to be even, which must be 6.

Therefore 3 and 5 will be the outer cards.

Since the Club lies to the right of the 3, therefore 3 has to be the outer card on the left-hand side. Also, since the Club is not in the middle, it has to be the outer card on the right which must therefore be the 5 of Clubs

 And since the 4 lies between the two black suits, hence the card adjacent to the 5 on its left will be the 4.

Therefore the 6 will be the second card from the left and will lie in between the 3 and the 4. Also, since on both sides of the 4 are black suits, hence it has to be the 6 of Spades.

Finally, since the Spade lies to the left of the Heart, therefore we conclude that the 4 is the Heart and therefore the 3 is the Diamond.

The final solution will look like this:

5.6      We are not used to juggling to-and-fro with data, and tend to throw us our hands in exasperation when confronted with something like this. Patience is not a major virtue of these times.

However, the moment we start putting down the data presented in a systematic manner, things immediately become clear.

Representing the facts given pictorially, the answer is: Tomorrow will be Friday.:

5.7      The plethora of facts presented can be bewildering to most, but putting down the facts and the conclusions in a logical order will immediately begin to untangle the puzzle:

  • Since both Shimla and Delhi are equidistant from Midway, hence the nearest neighbor of the Engineer will live in Midway town only.
  • Mr Y resides in Shimla so he cannot be the Engineer’s nearest neighbor
  • Mr. Z earns exactly 16lakh. Since 16 lakh is not exactly divisible by 3, hence the Engineer’s nearest neigbor will not be Mr Z
  • Thus, Mr X must be the nearest neighbor of the Engineer.
  • Therefore, the lawyer with the same name as the Engineer will be Mr Z. and hence, Z is the Engineer.
  • Since the Doctor was beaten by X, hence the only remaining person Y must be the Doctor.
  • Therefore, X is the Businessman

Not really as difficult as it looked at first, wasn’t it? We only had to follow a logical chain of thought and the solution just appeared!

5.8      Once again, let’s represent the facts given as a venn diagram:

One thing that is immediately clear is that if all Bings are Bongs, then it is impossible for some Bungs to be Bings without being Bongs. So the first statement is false.

The second statement will hold true in all cases, as can be seen in the diagram.

The third statement won’t hold if the above diagram looks like this:

Hence option (ii) is the only correct answer.

5.9      Let’s take it step-by-step:

  • Avid bowler is in Baltimore
  • Son who barbeques is not in Binghampton, hence barbequeing is happening in the third town which is Banbridge
  • Thus, Boating will happen in Binghampton

Now the situation looks like this:

Now, let’s place the brothers:

  • Bartholemew is not in Baltimore, and Benjamin is not the bowling enthusiast . Hence, the only option left for Baltimore is Barton.
  •  Since Benjamin is not in Bainbridge, he can only be in Binghampton.

Hence the third brother Bartholemew is the person who is barbequeing in Bainbridge.

5.10    Such problems require a methodical approach, meticulously organizing the facts in a fashion that helps to eliminate possibilities one by one.

Plotting the facts provided in a tabular fashion often helps. Let’s see how the situation looks after we have put in all given facts here:

The ‘x’ in black is an option eliminated due to a fact provided to us in the statements given, and the number following the ‘x’ gives the statement number containing the fact.

The ‘x’ in red are eliminated logically due to the statement whose number follows immediately after the x.

  • We see that only the Sergeant could be killed by the Shovel – Conclusion 1
  • We also see that the Pantry is the only place where the Captain could have been murdered – Conclusion 2
  • The Captain could only have been killed with the Gun – Conclusion 3
  • Only the knife could have been used to kill the Corporal- Conclusion 4

Now the situation looks like this:

  • Since the Knife was used on the Corporal, hence deriving from statement 4, the General could only have been killed with the Poker – Conclusion 5
  • And thus, the only weapon remaining is Poison, which was used on the Lieutenant – Conclusion 6
  • The murder weapons have now been finalized, and our chart now looks like this:
  • Now we know from statement 5 that the man murdered in the basement had dinner with the man done in with poison (General) and the victim of the poker (Lieutenant). Hence in the chart above, the only candidate remaining for the basement is the Sergeant – Conclusion 7
  • This also tells us that the only location available for the Lieutenant is the Bedroom – Conclusion 8
  • The final two locations available for the General and the Corporal are the den and the attic. Since Statement 3 tells us that the poker was not used in the attic, hence the General could only have been killed in the den – Conclusion 9
  • Thus, the Corporal was killed in the attic with the knife – Conclusion 10

5.11    We begin by arranging the already given facts in a table:

  • Jill doesn’t like Sundaes or Dry fruits, so they are crossed out
  • Sonu doesn’t like Sundaes
  • Amy likes Sweets – Conclusion 1
  • Abhi likes Chocolates and his birthday is in Feb – Conclusions 2 and 3.

From given facts, we can also eliminate a few possibilities. Since Amy’s birthday has to fall in the month immediately after Jill’s, hence Jill cannot be born in Jan as Feb is occupied by Abhi.

Hence Amy’s birthday cannot fall in Jan, Feb or March. Also, since the March born is the person who likes Pastries, hence Amy does not like Pastries. The initial table looks like this:

(figures in red show the eliminated options, cells shaded green are the finalized options)

  • The above table immediately tells us that the only option left for Jill’s favorite dessert is Pastries – Conclusion 4
  • Since we know that the person who loves Pastries was born in the middle month, hence Jill was born in March – Conclusion 5
  • Since Amy’s birthday follows that of Jil, hence it is in April – Conclusion 6

The situation now looks like this:

  • Since Sonu does not like Sundaes, hence the only available option for him is Dry fruits – Conclusion 7
  • Hence Bob is the person who likes Sundaes – Conclusion 8
  • The May-born likes Dry fruits, hence Sonu was born in May – Conclusion 9
  • Thus, Bob was the person born in Jan – Conclusion 10

5.12    The total number of medals is equal to 30, and the total sum of points available equals 60 (10gold*2+10silver*2+10bronze*1= 60)

  • Assuming sA, sB and sC are the sum of points won by A, B and C respectively, we are given: sA = sB+1 = sC+2

Also, sA+sB+sC = 60

Substituting the values of sB and sC in terms of sA, we get

sA+ (sA-1) + (sA-2) = 60

which implies, sA = 21. Therefore, sB=20 and sC=19

  • Assuming a,b and c is the total count of medals won by A, B and C respectively, we are given c = b+1 = a+2

Also, a+b+c = 30

Substituting in terms of c we get

(c-2)+(c-1)+c = 30

Which implies, c = 11. Therefore, b=10 and a = 9

  • This was the easy part. Now, we need to determine how many of which type of medal was won by each country. Let us take a look at the medal tally as it stands after our initial calculations:
  • We know that C won more gold than either A or B. Thus, neither A nor B could have won more than 4 gold medals, since if A or B was 5 then C would be 6 or more, which would take the total tally of gold medals over 10.
  • Also, the number of golds won by C cannot be less than 4, otherwise any one of A or B would have equal or more number of gold medals than C.
  • The only possible combination of medals with 3 or less gold and a total of 9 medals adding up to 21 points is 3gold+6silver = 9+12=21 points. Hence, the tally of A must be 3 gold and 6 silver.
  • We are left with 7 gold, 4 silver and 10 bronze for B and C
  • As C won more gold than A or B, hence B also cannot have more than 3 gold. The only possible option for B to win 20 points from 10 medals with maximum 3 gold and maximum 4 silver is 3gold+4silver+3bronze= 9+8+3=20
  • We are now left with 4 gold and 7 bronze = 12+7=19, which is the points won by C from a total of 11 medals.

Hence the final tally looks like this:

5.13    As usual, we start with plotting the provided facts in tabular form. Let ‘y’ represent a true fact, and ‘x’ represent an eliminated choice.

The preliminary table will look like this:

  • As there is only one female on every floor, and every floor has only two people, hence E, who works on the same floor as C – who is a male- must be the female – Conclusion 1
  • Since D is not on the 2nd floor, therefore the only floor available for her will be the 3rd floor – Conclusion 2
  • Thus, B and F will have to be on the 2nd floor – Conclusion 3
  • Since A,B and E are not in Personnel, and Admin has two people only, hence all three will be in Accounts only.- Conclusion 4
  • Since D – a female – is on the 3rd  floor, hence A – who is also on 3rd flr – will be the male – Conclusion 5

Now the interim table looks like this:

  • Since all females work in different departments, hence B must be a male: Conclusion 6
  • Therefore, F will be a female: Conclusion 7
  • Since all females work in different departments, hence F must work in Personnel: Conclusion 8
  • Finally, since Admin must have 2 people, hence C must work in Admin only: Conclusion 9

Thus, the final solution looks like this:

5.14    Depicting given facts as a venn diagram, we get:

Let x = total no. of males

A= married males who are under 30 =8 (given)

B = married males over 30

C = married females over 30

D= married females under 30

E=unmarried males over 30

F=unmarried females over 30

G =unmarried males under 30

H =unmarried females under 30

We are given: Total persons =70, Total married = 30, Total females = 30, Total above 30 = 24, total married males under 30= 8

Now we can derive the numbers from above diagram using the other facts provided:

  • Since 15 males are married, it means A+B = 15. Substituting the value of A =8, we get B = 7
  • 19 Married people are above 30 years. Thus, B+C = 19. Substituting the value for B, we get C = 19-7 = 12
  • 12 males are above 30 years. Thus, E+B = 12.  Substituting the value for B, we get E = 12-7 = 5
  • Since 30 out of 70 are females, hence x = total number of males =  40. This means, A+B+E+G = 40. Thus, 8+7+5+G = 40, which gives G = 20
  • Now, total people above 30 = 24 = B+C+E+F = 7+12+5+F. Thus, F= 0. This means, there is no unmarried female above 30.
  • 30 people are married. This means A+B+C+D = 30. Thus, 8+7+12+D=30, which gives D=3
  • There are 30 females, this means C+D+F+H = 30. Therefore, 12+3+0+H = 30, which gives H = 15

Thus, the final breakup will look like this:

5.15    This puzzle requires painstaking arrangement of all given facts and then elimination of the options one by one. It requires the patience of a saint to solve such puzzles, but is guaranteed to give a huge dose of satisfaction once you succeed.

Let’s start by first creating a table that captures the puzzle and the basic given facts:

  • Since the Norwegian lives next to the blue house, and his house is the first, hence the second house is blue.
  • Also, since the Brit lives in the red house, and the green house has to be immediately to the right of the ivory house, hence the Norwegian cannot live in the red, green or ivory houses too.
  • Hence, the Norwegian must live in the yellow house.
  • Since Kools are smoked in the yellow house, hence the Norwegian smokes Kools living next to the  blue house which has the horse
  • Since Milk is drunk in the middle house, the Ukrainian drinks Tea, the Lucky Strike smoker drinks orange juice, and the green house has the coffee drinker, so the Norwegian must be the water drinker.
  • The Japanese cannot live in the second house, because then he cannot drink coffee (green house), milk (middle house), orange juice (lucky strike smoker), water (Norwegian) or tea (Ukrainian).
  • The Spaniard has the dog,so cannot live in the blue house (horse). The Brit lives in the red house. This leaves only the Ukrainian for the blue house.
  • So, the Ukrainian cannot smoke Kools, Old Golds, Lucky Strikes or Parliaments. Hence he must smoke Chesterfields.

At this point we have reached a position where we must eliminate choices by testing out a couple of hypothesis.

  • If either the Japanese or Spaniard live in the middle house, the red house will have to be last house as the red house belongs to the Brit and the green house must be immediately to the right of the ivory house. Hence the ivory house will be the middle one in such a case.
  • If the Japanese were to live in the middle house, it will mean he drinks milk.
  • Since coffee is drunk in the green house, that will leave only orange juice for the red house (Brit)
  • That will mean the Brit smokes Lucky Strikes, leaving Old Golds for the Spaniard in the green house.
  • But the Old Golds smoker owns snails, whereas we know that the Spaniard is the owner of the dog, so this option is contradictory and is ruled out.
  • In case the Spaniard lives in the middle house, he owns the dog and drinks milk. Then the Japanese must be in the green house smoking Parliaments.
  • But the Spaniard cannot smoke Old Golds as he does not own snails, and he cannot smoke Lucky Strikes as he drinks milk. So he has no smoking option left, which is a contradiction and hence is ruled out.
  • Hence, we conclude that the Brit is the only possibility for the middle house. Then the Green house has to be the last as it has to be on the right of the ivory house.
  • The only drink available for the ivory house is thus orange juice. This means Lucky Strikes are smoked in the ivory hosue
  • Thus the Japanese will occupy the fith house (green), smoking Parliaments
  • Hece, the Old Golds are being smoked by the Brit, who is also the owner of the snails
  • The Spaniard, therefore, lives in the ivory house (4th) with his dog.
  • Thus the Norwegian owns the fox, living next to the person smoking Chesterfields, while the Japanese owns the zebra.

5.16    We start by establishing the dependencies of questions on each other. Once we know that, then we get the starting point of the reasoning process.

In this case, the first question is dependent on the second question. Also, the third question can be answered if we know the answers to both the preceding questions.

Hence, we start with the second question. We can see that the options for the first question mirror the answers for the second question, i.e. if we answer A to the second question then the answer to question 1 also becomes A, If the answer is B, then the answer to question 1 will also be B, and so on.  

Thus, we can easily see that option A for the second question is the only one that holds true for both question 1 and question 3. All other options are either contradictory or not possible for questions 1 and 3. Hence the answers to the three questions will be: A, A and C.

5.17     The questions given are:

  • Given Answer of Q 20 is E. Other options are therefore eliminated.
  • Then we can immediately rule out Option A of Q3, as number of questions with answer E will be definitely greater than zero.
  • Since, as per Q.2, the only two consecutive questions with identical answers range from Q.6 to Q11, hence option E for Q19 gets eliminated.
  • The answer to Q1 cannot be option A, so this is also ruled out.
  • The answer to Q5 must be E, which effectively states that the answer to Q5 is the same as the answer to Q5. Hence other options for Q5 are ruled out.
  • As per the negated options of Q5, the corresponding answers of Q2 (B), Q3 (C) and Q4 (D) also get ruled out.
  • Since Q2 (B) is eliminated, hence Q1(B) also is ruled out.
  • Since Q5 has the answer E, hence option Q1 (E) is also ruled out.
  • By ruling out Q2 (B), we also rule out the corresponding option of Q1 (B).

At this stage our solution grid will look like this:

  • Q10 and Q16 reference each other’s answers. We see that options Q10 (A) and A16 (D) are hold true, while the cross-references of the remaining options do not hold true. Hence the answers to these two questions will be Q10 (A) and Q16 (D). The other options stand negated.
  • After this, referencing the statement of Q2, we rule out options Q4 (E) , Q15 (D) and Q17 (D) as answers to consecutive questions after Q11 or before Q6 cannot be the same.
  • Q6 and Q17 also reference each other. Option E for both questions immediately gets ruled out as there are no multiple true answers to any question. Also, since we have already ruled out option  Q17 (D), hence the only cross-reference which logically holds is of Q6 (D) and Q17 (B). The other options for these two questions are thus eliminated.

At this stage out solution grid will look like this:

  • By Q1, there has to at least one question among the first five with an answer (B), Hence option Q11 (A) is ruled out. After this, we will also rule out option .Q2 (E), since the answers of Q10 and 11 are not the same.
  • By Q13, the only odd numbered questions that can have option A as answer are Q9,11,13,15 or 17. Therefore we can now rule out Q7 (A) and Q19 (A).
  • Now for Q13, option A is ruled out since if Q9 had A as an answer, then no other odd number question will have option A as answer, and Q13 itself is odd. Thus, we rule out A9 (A) and Q13 (A).
  • Q13 (C) is also ruled out, since Q13 cannot have both A and C as answer. We have also already ruled out Q11 (A) and Q17 (A) previously, hence the only option remaining for Q13 is D.
  • Referencing Q13 (D), we now know that the answer to Q15 will be A.
  • Q15 (A) references the answer to Q12, which must therefore be Q12 (A). Other options of Q15 and Q12 are eliminated.

Now the solution grid will look like this:

  • We are getting close to the final solution. Since we have already eliminated Q8 (A), therefore Q2 (D) also gets eliminated.
  • By Q12, since the number of questions with a consonant as the answer is an even number, hence the number of questions with a vowel as the answer must also be even as the total number of questions is even. Hence we eliminate options B and D of Q8.
  • Since we already have a total of 5 answers which are vowels, hence option Q8 (A) also gets eliminated.
  • Also, since we already have two answers with E as the answer, so Q3 (B) also gets eliminated.
  • Since we know that Q5 has E as an answer, hence Q1 (E) is eliminated.
  • With this, the only remaining answer for Q1 is D, which means that Q4 is the first question which will have B as the answer.

The grid will now look like this:

  • Now Q4 (B) tells us that there are 5 questions with A as the answer which is an odd number quantity. Since we have previously concluded that the number of vowels as an answer has to be even, it follows that the numbers of questions with E as an answer must be odd (since odd + odd = even).
  • Thus the answer to Q3 must be D, since option Q3 (E) has the value of 4 which is even and hence must be ruled out.
  • Now from Q3 and Q4, we know that the total number of questions with a vowel as a solution is 3+5 = 8. Thus the answer to Q8 will be option E, and option C stands eliminated.
  • Since we now already have 3 answers for option E, which is the maximum as per Q3, hence all other E options of remaining questions stand eliminated.
  • Now, for Q9, option C gets ruled out, since the answer to Q12 is option A.
  • Also, we already have an option B as the answer to Q4, hence option B for Q9 gets ruled out, because in this case there will be two option B answers before Q11 which will then become contradictory.
  • Thus the only option remaining for Q9 is option D.
  • Since the answers to Q8 and Q9 are not similar, hence option C for Q2 now also gets eliminated, leaving only option A as the answer.
  • This means that Q6 and Q7 must have similar answers. Hence the answer to Q7 will also be option D, same as Q6.
  • Thus the only possible answer to Q11 is option B, and other options are eliminated.
  • Now, since we already have 7 answers as option D, hence Q14 (A) gets ruled out.
  • Since we know that there have to be 5 answers as option A, hence the answer to Q18 must be option A.
  • From Q18, since the number of option B answers must be equal to option A answers, hence both the remaining questions must have option B as the answer.

Thus, we reach our final solution grid, as shown below:

4. Numbers Don’t Lie

“A good decision is based on knowledge, and not on numbers” – Plato

Some of us love Maths and some hate it. Love or hate, we cannot deny that numbers are integral to our lives. We have to deal with numbers on a daily basis, and a number of times our proficiency in Numerical ability determines whether we win or lose in a situation.

Numerical ability does not really need a degree in Maths, nor does it involve complex mathematical formulae and concepts. It is something that even a middle school student can possess in adequate measure. You just need to set aside your fear of Maths and learn to trust your ability to do basic mathematical calculations.

Most of the puzzles which follow won’t even require putting pen to paper, and those that do will involve simple calculations mostly. What these puzzles will test, however, is the ability to grasp the basic concepts and to figure out exactly what you must do to arrive at the answer.

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4.1    This is a question from the Oct’ 80 SAT test, where there was supposed to be only one answer, but the people who prepared the test overlooked something which meant that the choices given contained two correct answers to this question. When this error came to light, those who had marked either of the answers were given full marks for this.

Can you find what the mistake in the below question-answer set was?

Which row contains both the square of an integer and the cube of a different integer?

(A) 7, 2, 5, 4, 6

(B) 3, 8, 6, 9, 7

(C) 5, 4, 3, 8, 2

(D) 9, 5, 7, 3, 6

(E) 5, 6, 3, 7, 4

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4.2    Complete the given number sequence:

1,2,4,7,11, ?, ?

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4.3    Think you are fast in doing calculations mentally? Lets see how quickly you can figure this one out.

The total cost of a bat and a ball comes to Rs. 230. The cost of the bat is Rs. 200 more than the ball. What is the cost of the ball?

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4.4    While you may choose to do this one through trial and error, but I recommend that you use logical reasoning or, alternatively, write it in the form of a couple of simple equations and solve.

Hint: Recall the basic divisibility rule for 9

Which is the smallest two digit whole number which is equal to nine times the sum of its digits?

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4.5    This puzzle is a classic one which forces us to suspend and overcome our initial disbelief in the premise of half a hen and half an egg before we can reach the conclusion.

A hen and a half lay an egg and a half in a day and a half. Can you tell how many eggs will half a dozen hens will lay in half a dozen days?

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4.6    The Binary notation challenges the way we are used to looking at numbers.  Breaking the shackles of conventional way of thinking also is one of the bigger challenges we often face when trying to figure out creative solutions to problems or when trying to innovate. Let’s give it a whirl now.

Take a look at the Binary notation for the decimal numbers 1 to 8 given below:

1=0001, 2=0010, 3=0011,4 =0100,5=0101, 6=0110, 7=0111, 8=1000

Can you say how the number 12 should be represented?

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4.7    On my way to the Himalayan abode of Abujhgarh, I met a man with 7 wives, each of whom carried 7 sacks. Each Sack had 7 hen and each hen had 7 chicks. Man, wives, sacks, hen and chicks, that’s quite a jamboree.

Can you tell me total how many heads were going to Abujhgarh? 

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4.8    Simple number puzzles expressed in sentences often leave us stumped. Once again, we get so used to seeing numbers as symbols and digits only, that many have a hard time relating the sentences to their numerical form. Such puzzles build up our powers of mental association and help in boosting our creative visualization processes.

There is a number from which if I subtract twice the cube of it then I end up with the square of it.

What is the number?

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4.9     Here is another simple puzzle that quite a few people find hard to comprehend, as they lose track of the reasoning process midway.

If 10 people eat 10 Burgers in 10 minutes, how long will it take for 35 people to eat 70 burgers?

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4.10 Just like magicians relying on distraction and sleight of hand to fool the audience into believing something that is not, there are some classic puzzles that rely on getting your thoughts so jumbled up using a clever play on words that you tend to lose track of facts in front of you. Give this one a try, and see how you fare:

Three friends went out to dinner at their favorite restaurant. There was a new steward who took their order. After the meal, the steward brought a bill for Rs 150, so the three friends contributed a Rs 50 note each. The Manager, who was just coming out of his office, recognized the three as old friends. When the steward returned with the payment, the Manager instructed him to return Rs 50 to them.

The steward was dishonest and returned only Rs 10/- to each friend, pocketing the remaining Rs 20.

So now, each friend has paid Rs 40, which comes to a total payment of Rs 120/-.  The steward has kept 20/-. This brings the total to Rs. 140.

Where did Rs. 10 disappear?

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4.11 Number sequences are a wonderful tool to build up our analytical reasoning skills. They encourage us to explore myriad ways a sequence of numbers may be related, and to distinguish patterns out of seemingly disparate elements.

What number should replace the question mark here?

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4.12 If the previous one was too easy, then have a go at this one:

There are two possible answers, can you get both?

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4.13 What numbers should come in place of the question marks?

18,26, 23, 23, 28, 20, ? , ?

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4.14 Making sense of a jumbled data is something we have to all the time at the workplace. Such puzzles improve our skill at organizing data. Be aware, though, that sometimes you really need to think beyond the usual in order to get to the solution.

Create an equation with only the elements given below. Each element must be used only once:

2, 3, 4, 5, =, +

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4.15 At times our concentration on performing calculations and getting to the result is so total that we fail to understand the problem itself.  Can you calculate the correct answer to this one?

A hungry monkey jumped down an almost dry well with slippery sides to get to some coconuts at the 30 feet deep base. Now it must climb out, but it is hard work. It can climb up 7 feet during the daytime every day, but then slides down by 6 feet every night while it tries to rest.

How many days will it take to climb out of the well?

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4.16 This is a puzzle that went viral a few years ago and has been immensely popular since then. There are two answers possible here, so even if you know one then try to work out the other!

1+4   =  5

2+5   = 12

3+6   = 21

8+11 =  ?

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SOLUTIONS TO CHAPTER 4

4.1      While the answer to this was only supposed to be (B) which contains the square of 3 and cube of 2, the paper-setters missed out on the fact that in option (C) there was the square of -2 (square of a negative integer is positive) as well a s the cube of 2, and both are distinct integers !

4.2      This is an easy one, with each successive number increasing by 1,2,3,4,5… and so on.  Thus, the next two numbers in the series will be 11+5=16 and 16+6=22

4.3      If you came up with Rs. 30 as the answer, then look carefully at the wording of the problem. If the ball is Rs. 30, and the bat is Rs. 200 more than the ball, then the cost of the bat itself will be Rs. 230, and hence the total will become Rs.260.

The correct answer is Rs. 15, which means that the bat is for Rs. 215.

4.4      This can be solved in two ways. One is by solving a simple equation. Since it is a two-digit number, the number can be represented as (10x+y), where x and y are the two digits.

Now, since the number is 9 times the sum of the digits the equation can be represented as (10x+y)=9(x+y), which implies that x=8y.

The only single digits that meet this condition are x=8 and y=1

Hence the number is 81.

The second way is by logical deduction. One basic property of any two digit multiple (actually, this is true for all multiples of 9) of 9 is that the sum of the digits always adds up to 9.

Since the number is 9 times the sum of the digits, the answer is 9*9=81  

4.5      1.5 hen =1.5 egg in 1.5 days. Half a dozen days is 1.5*4=6

Therefore 1.5 hen will lay 4 times as many eggs in 6 days.

Thus, 1.5 hen will lay 6 eggs in 6 days

Hence, 6 hen will lay 6*4= 24 eggs in 6 days.

4.6      Following the same sequence, 9 will be represented by 1001, 10 = 1010, 11=1011. Hence, 12 will be represented by 1100.

There is a methodology to work out how any number may be represented by its Binary equivalent. It goes like this:

  1. First  you determine whether the given number is even or odd. If it is even, then assign the digit 0 and if the number is odd, then assign the digit 1. This becomes the first digit from the right.
  2. Now, deduct this last digit so obtained from the original number, and divide the resultant by 2. Again see if the number is even or odd, and again assign the digit 0or 1 accordingly. This gives the second digit from the right.
  3. Repeat the above process till you finally get 1 or 0 as the resultant, when the process comes to a stop.

e.g.: Let’s represent 21 as a Binary: 

21 is odd, so the right-most digit is 1.

(21-1)/2=10, which is even, so the next digit is 0.

 Now (10-0)2=5, which is odd, therefore the third digit is 1.

Then (5-1)/2=2, so next digit is 0.

Finally, (2-0)/2=1.

Thus, 21 is represented by the Binary 10101

4.7      This one is a variation of the classic puzzle known as ’As I was going to St. Ives”, which began as a nursery rhyme in the seventeenth century, The puzzle was made famous by appearing in the movie “Die hard with a vengeance”, where the villain threatens to set off a powerful bomb unless Bruce Willis and Samuel Jackson can solve this is 30 seconds. Eventually they save the day with a second to spare. How did you fare on this one?

The answer is: Only one head is going to Abujhgarh: Me. I only met the group on my way up.

The puzzle tries to mislead you through all the 7s thrown in, which tricks you into trying to do multiple calculations.

4.8       The number is -1.

The cube of -1 remains -1, while the square becomes positive 1.

Hence as per the problem statement, -1 – 2*(-1) = -1+2 = 1

4.9      Since ten people are eating 10 burgers in 10 minutes, it means each person has eaten one burger individually in 10 minutes.

Hence, 35 people will eat 35 burgers in 10 minutes only.

Therefore, 35 people will eat 70 burgers in 20 minutes.

4.10    There is no vanishing money here.

The friends have paid 120/-, of which 100/- has been retained by the restaurant and 20/- has gone into the pocket of the dishonest steward.

Since the friends paid 120/- and they got back 30/- from the original 150/-, no money is missing.

The way the puzzle is worded misleads you into equating the amount got back by the three friends with the amount retained by the Steward.

4.11    This is a straightforward one. The numbers on the outer blocks increase in a clockwise direction by the amount of the number in the centre. Thus, the central number in the third figure will be 7

4.12    The two possible answers are 104 and 399.

In the first case, you will see from the first and the third figures that the central number is a simple sum of the three corner numbers. Thus, in the middle figure we add up the corner numbers:  56+36+12 = 104

In the second case, you will find that the numbers of the middle figure are the result of the multiplication of the corresponding figures in the first and the third figure. For example, 4*14=56. Thus, here we multiply the central numbers of the first and the third figures: 19*21 = 399

4.13    When you look closely, you will find that there are two alternating series here: +5 and -3. Hence the next two numbers in the series will be 33 and 17.

4.14    The solution to this is 32 =4+5

4.15    24 days. On the last day the monkey will climb 7 feet and climb out, so it will not slip back. Hence before this the monkey has to climb 23 feet which will take 23 days since its net climb rate is 1 foot per day.

4.16    The two possible solutions are given below.:

a) When we add the RHS of the previous line to the LHS of the next line, the equations balance. Hence in this case the answer will be 40.

1 + 4               = 5

2 + 5+5          = 12

3 + 6+12        = 21

8 + 11+21      = 40

:

b) The equations balance when we express the LHS as:

 First Number + (First Number * Second Number).

Thus, in this case the equations will become:

1 + (1 x 4)      = 5

2 + (2 x 5)      = 12

3 + (3 x 6)      = 21

8 + (8 x 11)    = 96

Hence, the answer in this case will be 96

3. Riddles and Puzzles: Taking Things at Face Value?? Buyer, Beware!!

Life is full of instances where what you see may not be what you actually get. People are out to deceive you at every opportunity, and our own tendency to assume too much or read too much into things sometimes leads to us getting duped royally.

The rapid-fire puzzles that follow have something in them to mislead you and put you on the wrong path. Can you avoid the traps and get to the solution?

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3.1    A man fell out of a twenty-four storey apartment building   window yet survived the fall without serious injuries. He was not Superman, so how did that happen?

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3.2 A Maths professor asked his students to tell him how much dirt was there in a 1ft x 2ft x 3ft hole. All except one student failed to find the correct answer. Can you say what is the correct answer?

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3.3 There was a cow tied to a rope of length 10ft. You had kept a bale of hay about 25 ft away from the cow. The cow was hungry but there was nobody present to help. Yet she managed to eat the hay. How was it possible for the cow to reach the bale of hay?

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3.4 Would you say that the product of the first ten digits lies between 100 to 1000, or should it be greater than 1000?

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3.5 Is it legal in any state of India for a man to marry his widow’s sister?

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3.6 Publishers of dictionaries are supposed to know better, but I’ve always found an error in every English dictionary I’ve seen. And there always is a word that is spelled incorrectly in every dictionary. Do you know which two words I am talking about?

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If you found the preceding rapid-fire round of puzzles too tame, the next set of puzzles should be much more intellectually stimulating, I believe!

3.7 The Sun is approximately 148 Million Km from Earth. This can also be expressed as 8.2 light minutes, as it takes light 8.2 minutes to reach the Earth from the Sun. The current speed of light is approximately 300,000 Km per second.

If we assume that daily sunrise time is at 5.52 am and something happened in the universe that the speed of light miraculously tripled to 900,000 Km per sec, what time will the sunrise happen tomorrow?

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3.8    Most of us have seen a lot in our lifetime, but certainly there still is a lot left to discover and learn. Now, do you know of a place where Monday comes before Sunday?

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3.9    You enter a bathroom and find the bathtub filled to the brim with water. You also see a short pipe, a gallon mug and a glass on the sink, and a very heavy iron bucket underneath it. How will you empty the bathtub in the least time?

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3.10  Addition isn’t always straightforward, it seems. Do you know, once I added two to eleven and got one as the answer! Would you know what am I talking about? 

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3.11  Two people want to cross a crocodile infested river. The only way to cross it is in a small boat tied on the side of the river, but the boat will only hold one person at a time. There is no way for the boat to get to the other side on its own, and there are no ropes which can be used to tow or pull it from the other side. Yet both persons cross the river safely. How is it possible?

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3.12  A man dressed completely in black was walking down a road which was also black. He was wearing a black turtleneck sweater over black jeans, a black balaclava, black gloves, and black sunglasses. 

The streetlights were off and there was no Moon. Suddenly a truck with its headlights off came careening down the road straight towards him. Yet the truck stopped before hitting him.

The truck driver was an ordinary person with ordinary senses and ordinary reflexes, so how did he know he had to apply the brakes?

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3.13  In the year 2015, a person was 30 years old but in the year 2020 the age of the same person was 25 years. How can this be possible?

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3.14  My piggy bank is tubular with one end closed and a diameter just marginally bigger than the diameter of a 1 Rs Coin. Each coin is 2mm thick, and the piggy bank has a depth of 18cm. How many1Rs coins can I place in the piggy bank until the piggy bank is no longer empty?

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3.15   Think it is an easy job designing a car? The quantum of Physics involved is mind-boggling. Now tell me this: which tire doesn’t rotate when a car makes a really sharp right turn?

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SOLUTIONS TO CHAPTER 3:

How many correct answers do you think you got?  Check out the solutions below, and don’t hate me for some of the answers:

3.1 The building may be high, but where does it say that the man himself was on the top floors? In this case he fell out of his first-floor window, and hence was not seriously injured.

We put on mental blinkers so many times, assuming conditions and making presumptions without being expressly told. Sometimes we need to just absorb facts as they come in, and judge accordingly.

3.2  Hole (definition): An empty space in some discernible medium. “Empty”, isn’t it? Well, there can’t be anything in an empty space, so the correct answer is: “Nil”.

You can still thank me for brushing up your Mensuration formulae, though, if you did go about making those volume calculations.

3.3  The cow was tied to the rope, but nowhere is it mentioned that the rope itself was tethered to anything else. All the hungry cow did was to simply amble over to the bale of hay and eat it.

The lesson from this is: Never presume! Keep an open mind and an active imagination.  

3.4 Zero is one of the first ten digits, and we know what happens when we multiply by zero. Hence the answer to this is 0.

Did you really go about multiplying all those digits and numbers? I didn’t say ‘Natural numbers’, did I? Its amazing how many of us are so prone to seeing only what we want to see and acting on only what we think to be true, despite facts in front of us.

3.5 Well, if a man has a widow, then he is certainly dead, isn’t he?. Whatever you may feel about politicians, I don’t think they will ever get around to making marriage laws for dead people in any state.

Such “gotcha” type of puzzles show us how people get blindsided by an overload of data and simply can’t see the obvious. Master politicians so often make use of this tendency to divert attention and debate away from the real issues facing people. 

3.6 The word “ERROR” will of course be present in every dictionary. And the word “INCORRECTLY” will always be spelt so wherever it is published.

Sometimes we really should take given facts at face value! 

3.7 Irrespective of the time and effort you may have put into calculating the time differential due to changes in speed of light, I feel obliged to point out that the time of sunrise has absolutely nothing to do with the speed of light.

It would have mattered only if the Sun were to act as a lightbulb with an on-off switch, in which case while switching on the Sun the rays would have taken their due time to reach Earth. Currently, the only thing affecting time of sunrise is the rotational speed of the Earth about its axis, which hasn’t changed. The sun will still rise at 5.52am, just as usual.

In life, you will so often find obfuscation as the resort of those who don’t want you to see or realize the obvious truth. While the answer to this is a fairly straightforward fact that we all have learnt in our Middle School, the puzzle reels out a number of totally irrelevant facts and trivia to keep you mentally occupied and keep you from recalling this.   

3.8 The place where Monday will always come before Sunday is on the pages of a Dictionary.

We spend too much time seeking out complex solutions. Many times, simple solutions are the correct or the more elegant solutions. 

3.9 Well, the usual way of emptying the bathtub by pulling the plug will be quickest, don’t you think? Or do you really see yourself throwing bucketfuls of water down the drain with that heavy iron bucket?

Learn to look beyond diversions! Once again, the puzzle has a number of irrelevant facts in it to serve as a distraction. You must learn to weed out the irrelevant facts, and take into considerations only the facts necessary to arrive at a solution to a problem in life or at work.

3.10 I was adding time, of course:  When you add 2 hours to11 am, you get 1 pm as the answer.

Many a time, you will face a problem where some of the facts are implicit and not spelled out loud. When the obvious ways of getting to a solution fail, you need to consider alternatives: cases where the implicit facts will match what has been laid out before you. This would be another instance of thinking out of the box.

3.11 The two people were on opposite banks of the river, of course!  The person on whose end the boat was tied took it and crossed the river, then the other person took it and crossed safely too.

In this puzzle, once again many of us find ourselves the victim of strait-jacketed thinking. We narrow our focus so much that we fail to consider all possible alternatives. We must broaden our horizons. Never presume that restrictions to any of the possibilities are present, unless it is explicitly mentioned so.

3.12 The puzzle only insinuates, but never mentions we are talking about night-time. Everything given is valid for daylight: There will obviously be no moonlight, no streetlights and no headlights during the daytime. And the driver would have seen the man clearly in broad daylight. Thus, he stopped in time.

Here too, the imagery the wording of the puzzles conjures up in our minds is of blackness and darkness, but we need to be mindful of facts that are not explicitly given. The puzzle tricks us into coming to conclusions which are in a totally different direction from the truth. Once we begin to recognize this, the answer becomes glaringly obvious.

3.13 When we see that the man’s age is actually decreasing even though the years seem to be passing, this should tell us we are not talking about ordinary times. However, our conditioned thinking stops us from pursuing this line.

The only time in history when years get counted backwards was during the BC period. Hence it is obvious that we are talking about the year 2020 BC and 2015 BC, with 2015BC coming after 2020BC. Now we can calculate that the man was born in 2045 BC.

3.14 The moment I put in 1 coin, the piggy bank does not remain empty. How many coins did you calculate, by the way?

You see, all the ado about the dimensions and shape of the piggy-bank was merely a distraction to keep you from seeing the obvious. Smokescreens are the favorite resort of all tricksters, so you must learn to spot and evade them. That will stand you in good stead at work and in life too.

3.15 The spare tire, of course. If you believe your car can pivot completely on one stationary tire, you are watching too many fast & furious movies.

Common-sense is not so common anymore. We are far too used to complexities in life and convoluted ways of thinking nowadays. A good start would be to start relying on our common sense once again. That could really change a lot of things in our lives! 

2. The World of Riddles and Puzzles – Seeing is Believing?

Visualization is integral to a solution seeking mindset. It is our ability to see and understand a problem in our mind, discerning patterns and inter-relationships. It utilizes the occipital lobe, which is the central point of processing the information by our brain.

The one trick all “Super Memory” gurus teach you is to visualize and associate whatever you are hearing or reading with some sort of a mental imagery which you can easily relate to.

Mental imagery has a beneficial effect on many cognitive processes in our brain: memory, planning and organizing, sense of perception, attention to detail and even your motor control.

Being able to visualize how pieces of a puzzle fit together or form a coherent pattern immensely benefits our ability to solve problems even at the workplace, where we so often work with disjointed pieces of information.

The puzzles in this section will test your ability to visualize and will check your visual acuity and spatial awareness. Some may be straightforward, but most will include some trickery designed to deceive. Better be prepared: Seeing may not always equate to believing!

Yes, the first one really is a disguised visualization problem. Remember, try to relate things mentally to get a solution.

2.1    If the sum of three consecutive odd numbers is 75, can you tell me the smallest number of the three? Don’t put pen to paper for this. Trust your mind and do this mentally.

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2.2    This is a famous- though now fairly commonplace- puzzle, but still worth being included here.

Connect the 9 equidistant dots given below with four straight lines only, without lifting pen from paper.

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2.3    This one is for those of you who said: “Aha, I know the answer to this” for the previous puzzle”,

Do the same exercise with only 3 straight lines, keeping other conditions same.

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2.4    Just in case you still didn’t feel challenged enough, try this one: Do puzzle number 2.2 with only one straight line, other conditions remaining same.

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2.5    Each of the number sequences given below follows the same rule. Can you determine what will be the last sequence?      

57, 35, 15, 5

68, 48, 32, 6

39, 27, 14, 4

78, __, __, _ ?

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2.6    There is a famous test created by the German Gestalt psychologist Karl Duncker, as part of his thesis on problem solving and functional fixedness. It is also popularly known as the Duncker Candle Problem.

The task is to fix a candle on a vertical wall (a cork board) and then light it up so that the wax from the candle does not drip on table directly beneath. To complete the task, you are given the three things:

An unlighted candle, a box of matchsticks, and a cardboard box full of thumb tacks that can be pressed on to the wall above the table.

Can you solve the problem?

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2.7    There is a political prisoner in Cell 1 of a prison that has a unique structure where cells have interconnecting doors with adjoining cells so that prisoners can interact. As he has been declared innocent by the court, the prison authorities must release him. He wants to meet each of the other prisoners before he goes, so the prison authorities agree on one condition: he can choose his route through the prison, and he must meet each person exactly once. If this condition is not met, then he will be detained on charges of inciting prisoners.

Can you help the prisoner chart the route so that he can meet each person only once before he leaves? 

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2.8    Rearrangement puzzles from X to Y can be truly challenging and a source of endless entertainment. There are countless such problems out there, but this one by Henry E. Dudeney – who is hailed as one of England’s foremost creator of Logic Puzzles – is one of the more enduring ones ever since it came into existence in the 1920s. Also known as the water problem, it challenges you to rearrange 8 coins arranged in the form of an H into a figure resembling the letter O (H to O!) in only 4 moves subject to the condition that each coin on being moved must touch two other coins – and not more than two coins- where it is placed.

Can you solve the problem?

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2.9    I got this code in a letter, and could make neither head nor tail of it. Can you tell me how to decode this?

Son you agree your jive kicks heaven straight line then”

2.10 Here is another matchstick rearrangement problem. Convert below shape into three equal squares by moving only three matchsticks.

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2.11 This fish needs to change its direction. Can you achieve this by moving exactly three matchsticks?

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2.12 Guess the next three letters in the series

G T N T L _ _ _

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2.13 You are given a large pile of coins – the quantity is unknown – and are told that it contains exactly 21 coins which are heads-up, while the rest are tails-up. You are blindfolded and must select some coins from this pile and put them into another pile such that both piles contain the same number of heads-up coins.

By touching you cannot determine which side is heads or tails, and you certainly can’t see anything You have one chance to complete this task.

How can you successfully meet the challenge?

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2.14 Think of the color of snow. Then think of the color of clouds in a bright blue sky. Now think which color stands for purity. Finally, think of the color of a bright full moon. Now answer quickly: what do cows drink? 

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2.15 Have you ever seen how fish swim in formation? Now here is a group of ten fish swimming together, but then they realize that the order of the formation is wrong. Now how can the formation be corrected with only three fish changing their positions?

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SOLUTIONS TO CHAPTER 2

2.1      All you need to do here is to divide 75 by 3, which comes to 25. This gives you the middle number of the three. Hence the smaller number will be 23.

We do not always need to reach for the calculator or put pen to paper. Many a time you can solve a problem just by looking at it and trusting your mind to provide the answer.

Many problems in life are simpler than they look, if only we have faith in our own abilities.

2.2      This is a puzzle that has been used by countless management gurus across the world as a classic case of ‘out of the box’ thinking. Literally, this means you shed your inhibitions and extend your horizon beyond the artificial, imaginary or self-imposed limits defined by the dots in this puzzle, in order to reach the solution.

The solution goes somewhat like this:

However, don’t feel despondent even if you didn’t get to the solution. In a study that actually debunks the notion of ‘out of the box’ thinking as something  that can be tutored, the nine dot problem was presented to a group of people who were actually told that the solution lay in extending the lines beyond the dots.

Surprisingly, the results varied only by about 5% from the results of a control group who were not given any such hint. As a concept “out of box thinking” does seem very motivational and attractive but it is not really something that can be learnt. It is a habit more than a skill.

2.3       The solution to this requires some more angling and extending of the lines, with the solution looking as given below. As pointed out earlier, don’t feel bad if you didn’t get to the solution, you can still be perfectly capable of out-of-box thinking in other areas closer to your areas of interest.

Just develop the habit of exploring alternatives in everything you do in the normal course of life and try to do new things beyond a fixed routine.

2.4      This one has myriad possibilities, and you can let your creativity flow here.

One possible solution would be marking the dots on a large piece of paper and then folding the paper in a conical shape so that the third dot of the first line comes from behind in line with the first dot of the second line, and so on. Then you just pick up a pen and connect all the dots in one stroke.

Some suggest taking a pen with a wide enough tip to cover all three lines in one stroke, and then just drawing one line which covers all the points.

Some people simply fold the paper along the three rows as the ridges like an accordion and press the ridges tightly together so that the three rows coincide, and then draw a thick line through them.

Some just cut the paper into strips and place the strips containing the dots in a single row one after the other.

As I said, once you let your creativity run riot, the possibilities are many. The lesson from these three puzzles is to just let your imagination fly at times, and you may be able to find creative solutions to many problems which you may not have believed possible earlier.

2.5      Each number in the series is the resultant of the multiplication of the two digits of the previous number. Thus, the series will be:

78, 56 (=7*8), 30 (=5*6), 0 (=3*0)

Visually being able to recognize the apparent patterns or interactions between various components can really enhance our analytical skills in the real world. We just need to stop robotically looking for complex solutions and simplify things in our mind sometimes.

2.6      Functional fixedness is a mental block and a cognitive bias that prevents us from considering familiar objects as having any other use that what we are accustomed to in normal circumstances.

For example, the simplest solution to this is to affix the cardboard box holding the tacks to the wall, and then standing the lit candle in the box, which ensures that dripping wax stays in the box only.

Even without the box, one could consider tacking the candle vertically to the wall, while also tacking the matchbox to its base to hold any dripping wax, if the matchbox is wide enough.

When the box was given to the people with the tacks filled in it, almost everyone failed to perceive the box itself as something usable, so fixated were they on the fact that it was merely a container for tacks and had no other purpose.

However, Duncker found that when the participants were given the tacks and the box separately, most people could use it to solve the problem.

This is an important aspect we need to keep in mind, specially in situations with limited resources and the need to use whatever we have at hand to solve problems. At the workplace this mindset is invaluable.

2.7      The key to the solution lies in the fact that the prisoner can return to his room without violating the conditions laid down for his release. Thus, he comes back to his room after meeting prisoner no 2, and then takes the route as shown below:

2.8      Such rearrangement problems hone our spatial awareness and logical thinking skills. The challenge is to determine your starting point and to be able to discern mentally which elements should not change position, and which need to be moved.

2.9      The words in the given sentence sound similar to the number series starting with One, Two, Three…

Such problems train our mind to look for and establish connections between auditory and visual cues.  In a world full of diverse sensory experiences, this is another skill we must develop to the fullest.

2.10    One solution will be in line with the one given below. There are other similar solutions.

2.11    Move the matchsticks as given. Once again, the key is to first establish which pieces must stay static. When you can visualize this mentally, the solution becomes self-apparent.

2.12    The series consists of the first letter of each word of the problem statement itself.

The last three words of the problem statement are “In The Series”. Hence, the last three elements of the given series will be: I , T and S.

2.13    Of course, at first glance, this puzzle looks like a very complicated problem of Probability Theory. However, the solution is truly elegant in its simplicity.

All you have to do is to simply pick 21 coins at random from the original pile, and then turn over the coins.

And there is your solution!

How can this be? Assume you pick out 21 coins that have all tails-up coins only. This means all 21 heads-up coins remain the original pile. Now when you turn over the 21 coins you had picked up, all of them will be heads-up now. So both piles now have 21 heads-up coins.

Take the opposite case: Say you manage to pick out all he 21 heads-up coins, leaving only tails up coins in the original pile. Now when you turn over your 21 coins, all of them will become tails-up. Hence both piles will now have only tails-up coins.

This remains true for any combination of heads or tails up coins you pick up, which you can check out for yourself.    

2.14    Cows, like all animals, drink water, of course!

If you said milk, perhaps it is time for you considered revisiting grade school.

2.15    Once again, a deceptively simple problem that leaves many people scratching their heads for hours. But all it needs is a simple comparison of fish positions in the two figures.

When you compare the ‘From’ and ‘To’ positions, you need to first understand which seven fish will not change positions, rather than trying desperately to move various fish into different positions. The moment you understand this through visual inspection, you know that only the fish marked 1,2 and 3 have to move.

The movements of the three are as given below, to obtain the solution required.

The World of Riddles and Puzzles

During these testing times of Covid lockdowns, I re-discovered the joy of solving puzzles as I looked for ways to keep my kids occupied and away from computer games for as long as possible. Some choice puzzles are covered later on in this blog, you can skip the introduction and move straight to them if you want.

If there is one skill that every human needs to survive and thrive in this world, it is the ability to solve problems. Our whole existence is about facing up to the daily challenges life throws at us and beating them. In our professional life we need to constantly find creative answers to tough problems facing our organizations, else we’ll find it hard to continue there!

Interviews, examinations, aptitude tests et al are all formal ways of testing the problem solving and critical thinking skills of people. However, how many of us consciously work on honing these skills? We take them for granted, relying on our past experiences as we go along. We are never truly conscious of the fact that our thinking and reasoning faculties, our cognitive ability, and our memories stem from unique sequences of millions and billions of neurons firing away in different regions of our brain.

Sometime during the third decade of our life begins the slow, continuous, and indiscernible decline in the number of brain cells. Initially we can’t feel this attrition, although we do begin to demonstrate forgetfulness or unmindfulness at some stage.

Not everything degenerates, however. A major study tracking thousands of young people over a period of almost 50 years of their lives ascertained that some cognitive abilities like verbal ability, spatial reasoning, maths, and abstract reasoning do improve after the age of 30. Another major study just brought out that new neurons are being formed in the brains of even older people.

Our brains need not degenerate with age – even though the volume of the brain may start to shrink from the 30s – and can possibly be trained to improve further. Evidence is also growing that learning continues throughout life and, when faced with new challenges, our brains can reroute or form fresh neural connections even in advanced age.

You can see now why we must keep exercising our brain by subjecting it to fresh challenges. Of course, the glow of satisfaction -and the resultant boost in confidence – which comes from emerging victorious- is the icing on the cake!

This specially curated set of problems is designed to take you through various challenges to engage all parts of the brain. Be forewarned though: Some of the problems will appear deceptively simple- but looks can and will deceive.

Solving easy puzzles requiring little to no analytical skills has mostly recreational value and provides some amusement. We must move beyond them to problems requiring serious thought and effort, in order to build up and hone our creative and reasoning mental faculties.

Solving puzzles has been proven to have tons of beneficial effects: We gain confidence, learn to be at once intuitive & creative as well as logical & systematic, and we learn to explore. We begin to appreciate the possibilities of  multiple correct answers existing for a single problem, and also of multiple different paths leading to a single solution. We learn to spot deliberate mis-directions and obfuscations, akin to what we face in the real world now.

Like all good exercise regimens, we start with some warm-up to get you loosened up and ready for the heavy lifting further on.

  1. The Person with no name?

Somebody’s Mother is called Maria, a Scientist of some note. Maria has four sons, and the first three sons are called Alpha, Beta and Gamma. What do you think is the name of the fourth?

Solution: Such puzzles have intentional misleading and irrelevant facts stuffed in them that are meant to send you haring off in the wrong direction, while the answer hides in plain view. In this case, there is absolutely no need to mention the Mother’s occupation, which itself is a big giveaway. We are conditioned to link a scientist with scientific names like Alpha, Beta etc. Following this progression, we would logically conclude that the fourth son must be named Delta…

only he isn’t!

The fourth son is named ‘Somebody’, as clearly stated at the beginning of the problem statement itself.

Such problems force us to move out of our comfort zone of conditioned thinking. We begin to appreciate the perils of over-analysing: the solution was staring us in the face, if only we could see and accept the obvious.

Ready for another one? See if you can avoid the red herrings here.

2. An English Aircraft crashed right on the border of France and Germany. Can you say where should the survivors be buried?

Astonishingly, over 70% of people fail to get this one: hopefully forewarned would have forearmed you?

The answer to this one is: Why would you ever want to bury the survivors?

Visualization is something that many of us are extremely poor at. In the humdrum of our daily lives, we lose the ability to visualize things beyond the ordinary. The brain must conjure up images to link what we see or observe, which is not easy for everyone. A prolific Imagination is hardly the forte of most people nowadays.

Take the puzzle given below: Can you visualize the answer?

3. The Matchstick Contortionist

You have been given three matchsticks. Without breaking, bending or disfiguring the individual sticks, how can you form the number Nine with only these three matchsticks?

                                                                                 

Solution: Once again, there is a decoy in the form of the image given with the puzzle. The three matchsticks are shown arranged as the number 7. The subliminal suggestion is that the answer will be likewise. Despite the brain protesting that it is impossible for three matchsticks to be arranged to represent the numeral 9 while meeting all the conditions given, many of us continue to press on trying to figure out a solution. We simply forget or overlook the fact that nothing in the problem statement excludes Roman Numerals.

Solution: So, of course, there is a childishly simple solution to this:

Visualization also entails the ability to relate different things mentally. Normally, when we see what we know or recognize, we can relate what it is about. It becomes a bit more complex if the connection is not straightforward. Solving such puzzles needs creativity and sharpens our reasoning acuity as well.

Let’s see what you can make of the next puzzle:

4. Rebus, anyone?  

What familiar phrase does the below pic represent?

Solution: Could you see the relation? The picture can be broken down into some prominent components, and each can be described by a set of different words or phrases, so what we need to do here is to find the ones which combine to portray the overall idea as a logical phrase or expression.

Well done if you got the answer correct. And don’t worry If you didn’t. Most of the people draw a blank here.

Solution:The answer is: “Once upon a time”:  Once (Ones: multiple 1)    upon (the division line “ / ” )    a time (12:25pm)

We now move on to the next category of puzzles, which test our numerical ability. Nothing too advanced, but it is indeed surprising how many of us lose track of basic Mathematics as we move ahead in life. This ability is connected to the left side of our brain, and exercising the brain with basic calculations linked to logical reasoning is a great way to keep it agile.

Ready to test check how agile you are in this area? Then let’s move on to the next question: a devilishly simple one!

5. Not so Elementary, My Dear Watson!

Ok, you may be a business tycoon easily managing a business worth Millions without breaking a sweat, but can you give me the answer to this simple problem?

100÷5(3+2)-2=?

Solution: Did you get the answer to this as “2”?

Congratulations, you are joined by over 80% of people who arrive at the same answer.

But the answer still is wrong. Majority does not make ‘Right’!

Recall ‘BODMAS’, the fundamental rule taught in Elementary school?  Division comes before Multiplication!

The correct answer, therefore, is 98

Simple, wasn’t it?

Well, the tough ones will surely follow later, never fear. Can puzzle solving ever be complete without testing your reasoning faculties to the limit? It is surprising how difficult it has become in today’s age for people to hold a train of thought. It’s time we got back some of the mojo of deductive reasoning. It inculcates discipline and patience. Take, for example, the following question:

6. Find the ages

Two friends Vinesh and Shivam meet after a long time. Shivam tells Vinesh that he has three daughters. Vinesh then enquires how old are the daughters. Shivam gets into a mischievous mood, and challenges Vinesh to guess the ages through some clues. Vinesh, always up to challenges, accepts. So Shivam gives the first clue:

“The product of the ages of my daughters is 72”

Vinesh thinks over it for just a bit before declaring that there was simply too little data to go by. Shivam smiles and accepts this, and provides the second clue:

“The sum of their ages is equal to the sum of the digits of my car registration number”

Vinesh looks at the car, does some calculations, then shakes his head and says the information is still not complete. So Shivam provides the final clue:

“My eldest daughter is a big fan of Serena Williams”

At this Vinesh immediately jumps and provides the correct answer.

Can you guess the ages of the three girls?

Solution: Factors of 72 are 1,2,3,4,6,8,9,12,18,24,36 and 72. All possible unique combinations for multiplying them to get 72, and the sum of those three number combinations can be represented below as:

72*1*1 =     72               72+1+1=    74

36*1*2=     72               36+1+2=    39

24*3*1=     72               24+3+1=    27

18*2*2=     72               18+2+2=    22

18*4*1=     72               18+4+1=    23

12*6*1=     72               12+6+1=    19

12*3*2=     72               12+3+2=    17

9*8*1=        72               9+8+1=      18

9*4*2=        72               9+4+2=      15

8*3*3=        72               8+3+3=      14

6*4*3=        72               6+4+3=      13

6*6*2=        72               6+6+2=      14

As we can see, all the sums are unique except for two, where the sum is 14. When Vinesh added up the digits of the car number, the only reason he could not guess the ages is because he got the sum of 14 which had two possible combinations: 8,3,3 and 6,6,2

However, the moment Shivam uttered the word “eldest”, it told Vinesh that there is only one daughter of a greater age, effectively ruling out the 6,6,2 option.

Hence he correctly guessed the ages as 8,3 and 3

Other than deductive reasoning puzzles, there are also logical reasoning puzzles which require you to grasp the inter-relationships between multiple entities and work sequentially in order to arrive at a conclusion. Most people find it tough to work with so much rigor and give up midway. However, these problems are great for developing a logical thought process along with the tenacity and patience to hold on and get to the solution.

Here’s an example of such a sequential logic puzzle, try to work with a pen and paper on this.

7. Whose house?

You meet six people at a party at a friend’s house. They live in the same neighbourhood. Their houses are of different colors: Green, White, Blue, Yellow, Brown and Peach. They challenge you to figure out who lives in which house, with each person giving a simple clue to help you reach a conclusion.

Swati: The Green house belongs to me

Ram: Abraham is my neighbour to the South

Jack: I live in the fruity house and Jill’s house is on my side of the street.

Brahma: The Green house is to my West.

Abraham: The White house is to my North and the Brown house lies between us.

Jill: The Yellow and White houses lie on the opposite side of the street from my house.

Basis these statements, can you tell who lives in which house?

Solution: Let’s determine our starting point. A clue to this is in Abraham’s statement that the Brown house lies between his house and the White House in the North.

Our first conclusions from this are:

  1. the street runs in a North-South direction, with houses on East and West sides
  2. Abraham’s House, the White house and the Brown house are all on the same side of the street

What else is given in the clues? Swati lives in Green house while Jack lives in the fruity house, which can only be Peach. Jill lives on the same side as Jack, and the Yellow and White houses both are opposite to her house.

Hence the next conclusions we draw are:

  • Jack (Peach) and Jill both live across the street from the Yellow and White houses
  • Therefore, Yellow house is on the same side as White House, Brown house and Abraham’s House

We can hence conclude that Jill cannot live in the Green (Swati), Peach (Jack), White, Brown and Yellow houses.

Thus, our next conclusions are:

  • Jill lives in the Blue house.
  • The Peach and the Blue houses are on the same side, and across the road from them are at least three houses colored Yellow, Brown and White.

Now, if the Green house (Swati) were on the same side as the Yellow house, we would then have four houses on this side of the street. But as Brahma says that the Green house is to his West, it means it is across the road from him. This is impossible, as we know that in this case there will be only two houses on the opposite side: Jack (Peach) and Jill (Blue)

Hence we conclude that

  • Green house(Swati) has to lie on the same side as Jack and Jill, which must therefore lie on the left side of the street only.

Thus, now we have the three houses on the right: Yellow, Brown and White. Since Abraham says that the White and Brown houses are to his North, hence he must occupy the Yellow house.

We only have Ram and Brahma left to place now. As Ram has Abraham as his neighbour to the South, hence he must occupy the Brown house (remember, the brown house lies between the yellow and white house). Therefore, Brahma lives in the White house to the extreme North.

Final solution will look like this:

Beyond logic puzzles, we have another category which requires a lot of mental association, imagery and intuitive thinking. Riddles have been popular throughout the ages: being simple, fun and challenging for all.

So, let’s conclude this session with some brain juggling through a riddle.

8. Riddle me this

“I’ll run but never walk, I’ll gurgle but never talk

I’ve a bed but never sleep, I’ve a mouth but never eat”

What am I?

Solution: Ever heard of a River?

The puzzles discussed above were a miniscule sample from an ocean of puzzles available in the world. Developing a taste for solving challenging puzzles can provide countless hours of fun, while sharpening your mental faculties.

What more can one ask for ?