A teacher gave her students a short quiz, but after grading the test, she lost her grade book and the answer key. Here are five students' exams:

Paul's test:

1. eggs
2. evaporation
3. Alligator
4. a potato
5. teeth

Todd's test:

1. milk
2. transportation
3. Alligator
4. a kangaroo
5. teeth

Jason's test:

1. eggs
2. transportation
3. Crocodile
4. a kangaroo
5. ears

Alicia's test:

1. eggs
2. evaporation
3. Alligator
4. a kangaroo
5. teeth

Bebe's test:

1. milk
2. transportation
3. Crocodile
4. a kangaroo
5. ears

She did remember, however, that someone got all five questions correct, someone got four right, someone got three correct, another person got two questions correct, and one person got only one answer right.

Who got all five questions correct?

Paul's answers differ entirely from Bebe, therefore neither of them could be all right or the other would have to be all wrong.

If Todd had correctly answered each of the questions, it would follow that both Jason and Paul would have each answered two correctly.

If Jason had been the ace, both Alicia and Todd would have ended up with the same score.

Therefore the only possible perfect scorer could have been Alicia. And as it happens, the rest follows without paradox.

Posted by Eric on 2003-12-11 21:25:33