Tricky Logic Puzzle (V): How To Really Solve It? - A whiteboard-style graphic illustration showing a cat and dog above two mystery boxes labelled "Mystery Box 1" and "Mystery Box 2". On the surface of each of these boxes, there are two question marks "??" marked.

Welcome to the fifth entry in the tricky logic puzzle series. This time, you are dealing with two mystery boxes in front of you. Each of these boxes has a note with a statement written on it. The following are the conditions of the puzzle:

1. Only one of the two mystery boxes contains a dog.

2. Only one of the two mystery boxes contains a cat.

3. One of the two statements on the boxes is true, while the other is false.

Here are the statements on the two mystery boxes:

Tricky Logic Puzzle (V): How To Really Solve It? — A whiteboard-style graphic illustration showing a cat and dog above two mystery boxes labelled “Mystery Box 1” and “Mystery Box 2”. Each of these boxes has the following statements written on it: Mystery Box 1: “There is both a dog and a cat inside this box.” Mystery Box 2: “The dog and the cat are inside the same box.”
The mystery box statements — Illustrative art created by the author

Your task now is to figure out which box contains what. Do you think you can solve this puzzle?

Spoiler Alert

Beyond this section, I will be explicitly discussing the solution to this puzzle. So, if you wish to give it a try on your own now, I suggest that you pause reading this essay and do so now.

You can continue reading the essay once you are done with your attempt. All the best.

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Setting Up the Tricky Logic Puzzle — Organising statements

If you were perceptive, you would have noticed that there are two sets of statements in this puzzle. One set of statements refer to the conditions of the puzzle. These are necessarily true statements:

1. Only one of the two mystery boxes contains a dog.

2. Only one of the two mystery boxes contains a cat.

3. One of the two statements on the boxes is true, while the other is false.

The other set of statements is the one written on the mystery boxes themselves. The third condition from the above condition set requires that one of the following statements is true and the other is false:

Mystery Box 1: “There is both a dog and a cat inside this box.”

Mystery Box 2: “The dog and the cat are inside the same box.”

So, having organised these statements, we are now ready to proceed with the puzzle. The trick to solving this puzzle is to figure out which of these statements is true. If we do that, we can figure out which animal is in which box.

Eliminating Possibilities

At first glance, it appears that both mystery boxes have statements on them that say the same thing. In reality, they are similar but not the same.

If you observe closely, you will notice that mystery box 1 has a specific statement (about itself), whereas mystery box 2 has a general statement. When faced with such circumstances, a good approach is to just assume that one of them is true, and see where that leads us.

To start, let us assume that the statement on mystery box 1 is true. That is, we assume that there is a cat AND a dog inside mystery box 1. This assumption might appear like it breaks conditions 1 and 2. But that is not the case.

Condition 1 merely says that only one of the boxes contains a dog. Similarly, condition 2 says that only one of the boxes contains a cat. When we combine these two statements, it does not rule out the possibility of one box containing both animals.

So, if we assume that both animals are in mystery box 1 (that is, the statement on it is true), then based on condition 3, the statement on mystery box 2 necessarily needs to be false.

However, the statement on mystery box 2 states that both animals are in one box. This is true, which leads to a logical contradiction. So, our assumption must have been wrong, which means that the statement on mystery box 1 must be false.

The Solution to the Tricky Logic Puzzle

If the statement on mystery box 1 is false, then condition 3 requires that the statement on mystery box 2 is true. As we have discussed previously, this does not break conditions 1 and 2.

This leads us to just one possible solution. Both the cat and the dog are in the same box, and they are in mystery box 2. Therefore, mystery box 1 must be empty.

Tricky Logic Puzzle (V): How To Really Solve It? — A whiteboard-style graphic illustration showing both the cat and the dog inside mystery box 2. Mystery box 1 is empty.
The solution — Illustrative art created by the author

I hope you enjoyed solving this puzzle. Keep an eye on this space for more fun logic puzzles in the future!

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