A cat hides in boxes 1 to 5. Each night the cat must jump to an adjacent box. Each morning, you open a box to catch the cat. How can you catch the cat?

#### The riddle

A cat hides in five boxes numbered 1 to 5 and placed in a row close to each other. Each night the cat must jump to an adjacent box. It is playing a hide and seek game with you. Each morning, you open a box to catch the cat. The cat has special powers to read your mind and it will know beforehand which box you will open. It plans its jump accordingly to escape you.

How can you catch the cat and win the game of hide and seek?

**Time to solve the puzzle:** 30 minutes.

It is a hard puzzle and it will be a pleasure to solve it. Give it a try.

### Solution to Catch the cat hiding in 5 boxes riddle: Problem definition

First look at the puzzle is not promising. How can I win the game of hide and seek if the cat knows beforehand the box I will open next morning?

Then again, **what does it mean?** *Unless the game is winnable, the puzzle won’t have been there.*

Conclusion 1:Even though the cat knows beforehand which box I am going to open, I must be able to catch the cat at the end.

Again, the same question I ask myself, what does it mean? At the least, the fact established is,

Conclusion 2:I won’t be able to catch the cat by just opening any box next morning. The cat will know which box I am going to open.

So,

Conclusion 3:Without bothering about where the cat hides,I must open boxes one after the other so that the cat won’t have any other choice than to jump to the box I will open next morning,even though it will know that it will be caught and lose the game.

**That must be the only way I can win the game**—not by pure chance of opening a box and catching the cat, but **by well thought-out strategy of opening a series of boxes.**

Now I got interested. I understood what I have to do.

Conclusion 4:I have to analyze the pattern of cat’s jump systematically along with a sequence of my opening boxes one after the other to gradually corner the cat to jump into a single box I will open next morning.

**The problem and way to the solution is defined.** I have to give body to the strategy and create steps that will win me the game.

#### Solution to Catch the cat hiding in 5 boxes riddle: Stage 2: Analyzing end state

My usual approach to solving such a puzzle where a series of steps will solve it, is to **imagine the last step and analyze it. **This is the **powerful natural End state analysis approach of general problem solving.**

A critical question I ask myself.

Critical question:Which box must I open to find the cat at the last step?

Will it be any of the five boxes? *Any difference between the 5 boxes regarding jumping pattern of the cat?*

Of course, there is a very important difference.

Conclusion 5:The cat may jump to TWO adjacent boxes from the box 2, 3 or 4, but to only ONE BOX from box 1 and 5.

This must be a **critical pattern discovery.**

Conclusion 6:I must corner the cat to either box 1 or box 5so that in the night it will jump to a single box 2 or 4 that I will know.

Both the important boxes 1 and 5 are equivalent to each other. I decide to corner the cat in box 5 at the last step. By this assumption, the last box I will open is box 4 to which the cat would jump previous night from box 5.

With this intermediate decision made, I *turn my attention to which box to open first and which to open second.* I like to think in important chunks.

#### Solution to Catch the cat hiding in 5 boxes riddle: Stage 3: First trial to corner the cat

The first critical question at this stage I ask is,

Critical question:How can I corner the cat by opening a series of boxes?

I realize, this is the time to go deeper into details. To get the right answer, I must mentally **make a few trials and analyze each result.** If I get the final answer, I stop. If not, I ask the next question, analyze and get its answer. This is the *second powerful natural problem solving technique I use—the Question, analysis, answer or QAA technique.*

**As a first trial, with no preference, I open box 1.** This morning the cat might have been in any of the four boxes, 2, 3, 4 and 5. Which box should I open next? Any of the four other boxes? No, that I won’t do. That is the random way of doing things. No randomness can catch the cat.

Then which next box opening would fit into a systematic pattern?

*Persistent questioning leads me to an important conclusion,*

Conclusion 7:To avoid random opening of boxes,I should open tomorrow the box adjacent to the box I opened today.This decision makes good sense as the cat also jumps to an adjacent box. This strategy of opening a series of adjacent boxes should fit well with the cat’s jumping pattern and cut it off from rest of the boxes.

So **after box 1, I open next morning box 2.** Where can the cat be now? If it were in box 2 last night, it could be in box 1 or box 3. It can very well be in box 4 or box 5 as well. Number of possible boxes for the cat is still 4—not reduced at all.

**To catch the cat in minimum number of box opening, at the second step I should have reduced the number of possible boxes for the cat by 1.**

#### Solution to Catch the cat hiding in 5 boxes riddle: Stage 4: Second trial to corner the cat

Deciding that opening box 1 is not the best option, **I decide to open box 2 in the first morning as the second trial.** Number of possible boxes for the cat is 4—box 1, 3, 4 and 5.

Following earlier strategy, **I open next morning box 3.** Possible boxes for the cat are, box 2, 4 and 5. If it were in box 3 yesterday, it can be in box 2 or box 4 today. What about the possibility of the cat to be in box 1?

To be in box 1, the cat must have been in box 2 yesterday morning and night. And I didn’t find the cat in box 2 yesterday.

That’s how number of possible boxes is reduced from 4 to 3 the very second day.

I am hopeful of success and **open box 4 the third morning.** Possible boxes for the cat are, box 1, box 3, and box 5. The possible number of boxes is still 3, but at the least it has not increased. I still have control and I analyze the situation.

The cat today, the third morning, may be in box 1, 3 or box 5. From box 3 and box 5 it can jump to box 4 and from box 1 and box 3 it can jump to only box 2. **Next morning, the fourth, the possible boxes for the cat will be reduced from 3 to 2—box 2 or box 4.**

*The cat might know my mind, but now I have the cat in my grip.* **I will chase it and open box 4 again next morning so that it is forced to jump towards the box 1.**

Consequences of opening box 4 in the fourth morning:The cat must jump to box 2 last night as it knew that I will open box 4 this morning.

I will not give any escape route to the cat and *open the box 3 the 5th morning still chasing it towards box 1.*

Consequences of opening box 3 the 5th morning:The cat must jump from box 2 to box 1 as it knew beforehand that I will open box 3 this morning.

**The cat today and tonight is cornered in box 1 finally.** It knows I will open box 2 next, **the sixth morning**, but it will have no choice other than to jump to the same box 2 tonight.

The cat and I know for sure thattomorrow, the sixth morning, I will open box 2 and catch the catto win the game of hide and seek.

**Task for you:** Find at least one more way to catch the cat in six moves.

#### End note

Apart from deductive reasoning and choosing favorable courses of action, I have used two powerful general problem solving techniques—**End state analysis approach** and **Question analysis answer or QAA technique.**

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