During thecoronaviruspandemic, a lot of riddles and puzzles are going viral on social media while people shelter at home. One of these is the Square Room Cat riddle. Read on to learn more about the puzzle and the answer.
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The riddle typically reads like this:
In a square room there is a cat in every corner of the room.
In front of every cat there are 3 cats.
How many cats are there altogether?
There’s also another version that’s a little longer, but has the same answer.
In each corner of a square room is a sitting cat. In front of each cat, there are 3 cats, and on the tail of each cat, there is a cat. How many cats are there in the room?
Are you ready to read the answer?
Here’s the Answer
There are 4 cats total.
Why is that the case?
Because we’re talking about a square room, you should think of this from the viewpoint of a cat standing in a corner of the room, with his back to the corner and his eyes facing the center of the room. From his perspective, the three cats in the other corners are all “in front of him.” And of course, at the tail of each cat is the cat who owns that tail!
If the cat were standing in the corner with his face against the wall, then it would appear from his perspective that one of the cats was “next” to him rather than “in front of” him, leading you to think there could be a more complicated answer to having three cats in front of every cat. But the only logical way to consider the riddle is to picture each cat in the corner with his back to the corner, facing inward to the room, rather than trying to smoosh his face against the wall. From that angle, all the other cats in the room like they’re in front of him.
In fact, this is the only way to have a simple answer. If you tried to look at it from the perspective of a cat whose face was against one of the walls, then he might think one of the three cats was to the side of him, rather than in front of him. So then you’d need to add another cat to the room for each cat. But this would all go out the window if the cat then shifted and had his back to the corner. It’s really just simplest to consider that each cat is standing in the corner and facing inward to the center of the room.
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There’s an interesting discussion about this riddle on Quora. One responder argued that there’s no good answer. Aaron Arthurs wrote, in part: “The total number of cats in this square room will be in the range of 4 to infinity. Let’s break this riddle down… An important but missing piece of information is which way each cat from each corner is facing. If the four cats are all facing each other … there are still four cats in total… But if any one of the four cats turns and faces their respective corner, then there will be infinite cats (and infinite mischief). This is to meet the condition that each cat faces three cats. It is a result of recursion without a terminating condition.”
A similarly worded riddle also gives us the same answer. It reads: “How many cats are in a small room if in each of the four corners a cat is sitting, and opposite each cat there sit three cats, and at each cat’s tail another is sitting?” For this riddle, the answer is the same because we’re talking about a small room. The cats are so close together that each cat’s tail is bumping into another cat in a corner.