Can You Really Solve This Tricky Logic Puzzle? (II) - An illustration showing Matt, Can, and Cheat vertically listed in a column on the left hand side. On the right of each of them, an arrow points to a smaller toy version of each of them. Above each arrow, a pink circle with a black question mark inside is drawn.

I am back with yet another tricky logic puzzle for you. And guess what? Matt, Can, and Cheat are back at it again. In case you haven’t read my first essay in this series, Matt, Can, and Cheat are our very own in-house fictional puzzle characters.

Matt is a human being, Can is a puppy, and Cheat is a robot. Before we proceed with the puzzle, I would like to mention that this puzzle, like the first one in the series, is on the easier side as I am still gauging the format and user-response.

With the housekeeping taken care of, onward to our puzzle we go!

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The Tricky Logic Puzzle Setup

On a bright and sunny day, Matt, Can, and Cheat find themselves bored and lazing around. As Can snoops around the lawn, she discovers a hidden treasure box. She is quick to alert Matt and Cheat. They gather around as Can opens the mysterious treasure box.

Inside the box, they are pleasantly surprised to find three miniature toy versions of themselves. Naturally, they wish to play with their newly-found toy versions. But the question is, who gets to play with which toy?

They all collectively decide that each individual gets one toy only. Each of them has the following to say about the situation:

Matt: â€śCheat will take Toy-Matt if I take Toy-Can.”

Can: â€śCheat will NOT take Toy-Matt if I take Toy-Cheat.”

Cheat: â€śI am NOT taking Toy-Can and Matt is NOT taking Toy-Matt.”

Can You Really Solve This Tricky Logic Puzzle? (II) — An illustration showing Matt — a human being on the left, Can — A puppy at the centre, and Cheat — a robot on the right. Mat says, “Cheat will take Toy-Matt IF I take Toy-Can.” Can says, “Cheat will NOT take Toy-Matt IF I take Toy-Cheat.” And Cheat says, “I am NOT taking Toy-Can and Matt is NOT taking Toy-Matt.”
Statements from Matt, Can, and Cheat — Illustrative art created by the author

Given this premise, your challenge is to figure out who gets which toy in the end. To this end, assume that ALL of them are telling the truth.

Spoiler Alert:

If you wish to solve this puzzle on your own, I would suggest that you pause reading this essay at this point.

After you attempt to solve the puzzle, you may come back and resume reading. After this section, I will be explicitly discussing the solution to this puzzle.

The Solution Approach

In the first entry of the tricky logic puzzle series, I covered how one could solve such logic puzzles using two general approaches:

1. The top-down approach.

2. The bottom-up approach.

On the one hand, the top-down approach deals with generalising possibilities and eliminating them one by one based on the information collected.

On the other hand, the bottom-up approach deals with cumulatively collecting information until we narrow down to a logical conclusion.

For this puzzle, I will be deploying both approaches simultaneously and approaching the solution from both ends. If you find this theoretical stuff boring, worry not. We shall get practical next.

Gathering the Information at Hand

The first important thing to note is that ALL three individuals are telling the truth. So, we can directly start applying logic based on each of their statements. This lets us approach the solution from one end.

Next, let us consider the nature of each of their statements. Both Matt’s and Can’s statements are “IF-Statements”. That is, they assert Cheat’s behaviour conditional upon their respective choices.

Cheat’s statement describes both his own choice as well as Matt’s choice. These statements let us approach the solution from the other end.

Let us now proceed to analyse the information at hand and build a mental model based on our analysis.

Analysing the Information at Hand

Cheat’s statement is not conditional, and hence the most straightforward.

“I am NOT taking Toy-Can and Matt is NOT taking Toy-Matt.”

– Cheat

The only trick to this statement is that it uses negation. But if you undo the negation, it reveals the following two facts:

1. Cheat is NOT taking Toy-Can → The only other options available to Cheat are Toy-Matt and Toy-Cheat.

2. Matt is NOT taking Toy-Matt → The only other options available to Matt are Toy-Can and Toy-Cheat.

We have now narrowed down the range of options for two individuals by analysing just one statement.

Moving on, here is what Can had to say:

“Cheat will NOT take Toy-Matt if I take Toy-Cheat.”

– Can

Using the information we deduced from Cheat’s statement, we could just transform the above statement into the following logic model:

IF Can takes Toy-Cheat → Cheat cannot logically take any other toy.

So, the only conclusion we can draw from this is that Can did not take Toy-Cheat.

Finally, here is what Matt had to say:

“Cheat will take Toy-Matt if I take Toy-Can.”

– Matt

Similar to ho we treated Can’s statement, Matt’s statement can be transformed as follows:

IF Matt takes Toy-Can → Cheat will take Toy-Matt.

Now that we have analysed all the pieces of information we have, we are now ready to solve the puzzle.

The Solution to the Tricky Logic Puzzle

Let us begin by assuming Matt’s statement. That is, let us assume that Matt takes Toy-Can. As a result, Cheat will take Toy-Matt. As a further consequence, Can would have no other option left other than to take Toy-Cheat.

But based on Can’s statement we know that Cheat will Not take Toy-Matt if Can takes Toy-Cheat. Furthermore, we already know from our analysis that Can did not take Toy-Cheat. Therefore, this leads to a contradiction and cannot be the case!

Since Matt cannot take Toy-Matt (based on Cheat’s statement) and the assumption that Matt takes Toy-Can leads to a logical contradiction, there is only one other solution. Matt can only take Toy-Cheat.

As a result, Can and Cheat have to choose from one of the two remaining toys: Toy-Matt and Toy-Can. From Cheat’s statement, we know that Cheat is Not taking Toy-Can. Therefore, Cheat is taking Toy-Matt and Can is taking Toy-Can.

So, all information considered, here is our solution:

Matt is taking Toy-Cheat.

Can is taking Toy-Can.

Cheat is taking Toy-Matt.

Can You Really Solve This Tricky Logic Puzzle? (II) — An illustration showing Matt, Can, and Cheat vertically listed in a column on the left hand side. On the right of each of them, an arrow points to a smaller toy version of each of them. Matt has Toy-Cheat on his right, whereas Can has Toy-Can, and Cheat has Toy-Matt respectively on their right-hand sides Above each arrow, a pink circle with a black tick mark inside is drawn.
The solution to the tricky logic puzzle — Illustrative art created by the author

Among the three of them, Can is the happiest because she gets to play with her own toy version. Who knows if this is the reward from the mysterious treasure box to its original finder?

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