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?

This is probably not the most efficient algorithm, but in this case it worked properly.

I assumed Paul got them all right and made a table of who got what right and wrong.

Q1 Q2 Q3 Q4 Q5 # RIGHT
Paul R R R R R 5
Todd W W R W R 2
Jason R W W W W 1
Alicia R R R W R 4
Bebe W W W W W 0

we know nobody got all the answers wrong, so one of pauls answers must be wrong. looking at the table i quickly saw that if paul got question 4 wrong then the number of correct solutions would be Paul 4, Todd 3, Jason 2, Alicia 5, Bebe 1; which satisfies the criteria for the solution.

I guess I got lucky only having to invert one column, but one could make a matrix and just keep inverting columns until the solution presented itself.

Posted by Phil on 2004-02-01 21:43:25