31 students in a row were numbered 1,2,...,31 in order. The teacher wrote down a number on the blackboard.

Student 1 said "the number is divisible by 1",
Student 2 said "the number is divisible by 2",
and so forth...until
Student 31 said "the number is divisible by 31".

The teacher remarked: "Very well pups, but two of you gave a wrong statement, and those two sit besides each other". Determine those two.

I wrote down all the numbers from 1 to 31 and for each one, I noted the all prime divisors of it.

My hunch was that one of the two numbers I was looking for was a prime, so I looked for a prime one of whose neighbors could be eliminated without taking away the divisors needed for any other number.

(Like for example we can't eliminate six because that will cause us to eliminate either 2 or 3, triggering another chain of eliminations)

Posted by levik on 2002-05-03 02:18:36