A, B and C just finished their breakfast. One of the boys had apples, another bananas and the third, grapes. If only one of the following four statements is true, who had what for breakfast?

C had bananas.

C did not have grapes.

B did not have grapes.

B did not have apples.

Call the sentences 1,2,3,and 4 respectively.
If 1 was true,then 2 has to be true.
That makes two truths,which is contradictory to the problem.
Therefore,1 is false,so we establish the fact that C did not have bananas.
Suppose B had bananas.
Then 3 and 4 would be both truths,which is contradictory to the problem.
Therefore,B did not have bananas,so A had bananas.
We will call the fact that A had bananas the important fact.

Posted by Tim Axoy on 2003-03-24 07:12:22