Can You Really Solve This Tricky Logic Puzzle? - An illustration showing Matt - a human being on the left, Can - A puppy at the centre, and Cheat - a robot on the right. All three of them are seen saying "HELLO!" together.

I recently came across a tricky logic puzzle that caught my eye. So, I thought I’d write about it. It’s on the simpler side, but it made me think and engage. If you are into logical thinking and problem solving, this puzzle should be right up your alley.

Our puzzle starts with three fictional characters: Matt â€” the human being, Can â€” the puppy, and Cheat â€” the robot. As Matt and Cheat are chilling, Can comes to them and complains that she has lost her ball.

Each one of them has the following to say about the situation:

Matt: â€śExactly two of the three of us are lying.”

Can: â€śI lost my ball.”

Cheat: â€śExactly two out of three of us are liars.”

Can You Really Solve This Tricky Logic Puzzle? — 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, “Exacty 2 of 3 of us are lying!” Can says, “I lost my ball!” And Cheat says, “Exactly 2 out of 3 of us are liars!”
Matt, Can, and Cheat — Illustrative art created by the author

Given these statements, your challenge is to figure out who is lying and who is telling the truth. Do you think you can solve this puzzle?

Spoiler Alert

If you wish to solve this puzzle on your own, I would suggest that you tune off of this essay now, and give it a try.

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

This essay is supported by Generatebg

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Gathering the Information at Hand

First things first, let us gather all of the information we have at hand. There are three individuals involved. Out of the three, two make direct statements on the truth of their claims.

The third one is Can, the puppy. She claims that she has lost the ball. Since she says nothing about the truth of any of the statements, let us ignore her for now and focus on the other two.

The next thing to note is that although Matt and Cheat have used different words, they claim the same thing; their statements are equivalent. Therefore, there can be only one possibility: either both of them are lying or both of them are telling the truth.

If one of them is lying and the other is not, it would lead to a logical contradiction. Next, let us continue analysing other possibilities.

Analysing the Tricky Logic Puzzle

If both Matt and Cheat are telling the truth, their claim(s) require(s) two liars. However, there is only one individual left as part of the equation (Cheat). Since this is logically not possible, they must both be lying.

The fact that they are lying requires the negation of their statement(s) to be true. Since they both claim that exactly two out of the three of them are liars, the number of liars in truth is either less than two or more than two. In other words, either one of them is a liar or all three of them are liars.

The Solution to the Tricky Logic Puzzle

We already know that both Matt and Cheat are lying. So, the possibility of there being only one liar goes straight out of the window.

Consequently, the only other possibility is: All of them are lying! There you go. That’s the solution to this logic puzzle.

Closing Comments

When it comes to solving such puzzles, there are two general approaches that one could follow:

1. The top-down approach.

2. The bottom-up approach.

In the top-down approach, one first lists down all of the possibilities and then eliminates them one by one based on the information collected.

In the bottom-up approach, one builds a cumulatively more accurate model of the truth with each piece of collected information until one is able to construct a valid logical conclusion.

In short, the top-down approach starts with possibilities and focuses on eliminating them, whereas the bottom-up approach starts with collecting information and focuses on arriving directly at a logical conclusion.

Can You Really Solve This Tricky Logic Puzzle? — An illustration showing Matt — a human being on the left, Can — A puppy at the centre, and Cheat — a robot on the right. All three of them are seen saying “BYE BYE!” together.
Matt, Can, and Cheat — Illustrative art created by the author

Now, can you guess which one of these approaches I employed to solve this puzzle? Which approach did you use intuitively?

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