Five children were playing kickball. One of the five broke a window. When questioned about the incident, each child made three statements of which two were true and one was false. The statements are given below.
Joe:
1. I didn’t do it.
2. Sally will tell who did it.
3. One of us is in big trouble.
Matt:
1. Joyce did it.
2. I didn’t do it.
3. I don’t even like to play kickball.
Vince:
1. I didn’t do it.
2. Joyce and I are good friends.
3. Sally doesn’t know who did it.
Joyce:
1. Matt lied when he said I broke the window.
2. I never saw Vince before today.
3. I never broke a window in my life.
Sally:
1. I saw Joyce break it.
2. I didn’t break the window.
3. I want to go home.
Who broke the window?
Vince did it.
Joyce’s statements 1 and 3 must be true. If she had broken the window, both statements would have been false. But since each child told only one lie, these two statements must be true. Therefore, Joyce’s statement 2 is the one that is false.
The statement of all the other children can then be proven true or false using this information.
Since we know that Joyce’s statement 2 is false, Sally’s statement 1 and Matt’s statement 1 have to be false. Joe’s statement 2 has to be false, since Sally did not tell who did it. Now we are left only with Vince.