ZOOM . zingers | PBS Kids

From Kristen, age 9 of CA:

Three kids are asked to stand in a straight line facing the same direction. The second kid can see the back of the first, and the third kid can see the back of both the first and the second. They each have a shape on their back. On the back of the first kid is a circle. On the back of the second kid is a square. On the back of the third kid is a circle. The 3 kids are then given the following information: "Each of you has a shape on his/her back. You either have a circle or a square. There are two of one shape and one of the other." With just this information who will figure out what shape is on his back first? Who will figure out what shape is on his back second?

Answer below...

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The kid in the middle figures he has a square on his back
first. Here's why. He figures that if the third kid (the one
behind him) saw two of one shape (on his back and on the
first kid's back) he would instantly know he had the other
shape on his back and would say so. Since the third kid is
not saying anything, he must be seeing one of each shape.
Since the second kid sees a circle on the back of the kid in
front of him, he must have a square on his back.
He says so. The first kid uses the same logic. Since the second kid (the
kid behind him) says he has a square, the first kid
concludes he must have a circle on his back.
Amazingly,
the third kid is the only one who can see two shapes but cannot
figure out logically what is on his back.

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