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 “**I**n **T**he **S**eries”. 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.