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:
- eggs
- evaporation
- Alligator
- a potato
- teeth
Todd's test:
- milk
- transportation
- Alligator
- a kangaroo
- teeth
Jason's test:
- eggs
- transportation
- Crocodile
- a kangaroo
- ears
Alicia's test:
- eggs
- evaporation
- Alligator
- a kangaroo
- teeth
Bebe's test:
- milk
- transportation
- Crocodile
- a kangaroo
- 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?
The student answering 5 questions (q) and and the student answering 4 q correctly must have precisely 4 common answers.
Now, comparing the comb(5,2)=10 pairs of students we note that only Paul and Alicia has precisely 4 common answers.
Therefore, either Paul or Alicia answered all questions correctly.
Assume that Paul answered all questions correctly. Then, he must have at least one answer common with each of the other 4 students. However in reality, he and Bebe has NO answers common between them. This contradicts the given conditions.
Assume that Alicia answered all questions correctly.
Then, we observe that, she has:
With Paul ........ 4 answers common
With Todd .........3 answers common
With Jason .......2 answers common
With Bebe .........1 answers common
In other words, Alicia answered all 5q correctly.
She was followed by:
Paul (4q), Todd (3q), Jason(2q) and Bebe (1q).
Edited on January 25, 2022, 9:27 am
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