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.
- 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?
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.
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:
- the street runs in a North-South direction, with houses on East and West sides
- 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 ?