MathDB

There are five smart kids sitting around a round table. Their teacher says: "I gave a few apples to some of you, and none of you have the same amount of apple. Also each of you will know the amount of apple that the person to your left and the person to your right has." The teacher tells the total amount of apples, then asks the kids to guess the difference of the amount of apple that the two kids in front of them have.

a)

If the total amount of apples is less than

16

, prove that at least one of the kids will guess the difference correctly.

b)

Prove that the teacher can give the total of

16

apples such that no one can guess the difference correctly.

Problem Statement