The Viral Logic Problem Melting Brains on the Web: 'The Cat and the Hats'

Here we go again: a problem spreads across the web, goes viral instantly, and endless threads break out on social media as everyone fights over the solution. These challenges are supposed to be fun, but lately they're the perfect spark for full-blown flame wars. What does NeoTeo propose? Review the riddle, explore its possible solutions, and enlist a math expert to spot any errors. In a word: learn.

A cat and three hats

There are no boxes or quantum variables here. The cat, playful as it is, hides in one of the hats, and to solve the riddle we must guess which one. Obviously, we're missing information, and the riddle gives us the following clues:

1. Hat 1 tells us: "The cat 'is' in this hat."
2. Hat 2 tells us: "The cat 'is not' in this hat."
3. Hat 3 tells us: "The cat 'is not in the first hat'."

But that's not all: only one of these statements is true, and the cat hides in a single hat. In other words, we can't have 'two truths' or think about multiple cats or the cat changing position. The answer options are five: Hat 1, Hat 2, Hat 3, None, or Insufficient Information.

If you think you can solve it, now's the time to try it on your own. Otherwise, we invite you to explore the solution with a video by Presh Talwalkar, on the channel Mind Your Decisions:

Solving the riddle

From the start, we can rule out that the cat is in the first hat. If clue 1 is true ("The cat 'is' in this hat"), then clue 2 would also be true ("The cat 'is not' in this hat"), and we can't have 'two truths.'

The same happens when we examine the third hat. If the cat hides there, clue 3 is true (The cat "is not in the first hat"), and that truth extends to clue 2 ("The cat 'is not' in this hat"), so we fall into the two-truths trap again.

Now, what if the cat hides in the second hat? Clue 2 ("The cat 'is not' in this hat") would be false, and clue 1 ("The cat 'is' in this hat") would also be false, leaving us with a single truth, which is clue 3 (The cat "is not in the first hat"). With one truth and two lies, the riddle is solved: the feline hides in the second hat.

Why do people get confused with this logic exercise? Maybe there's a small bias here: prioritizing truth over lies. That causes them to lose sight of the cat, so to speak, and not consider the possibility that the key remains hidden in a false statement. I hope you enjoyed it; please don't throw stones (?), and if you have a similar riddle to share, leave a comment!