A and B are two positive integers such that:
1. The number 59 can be made by adding nonnegative integral multiples of A and B in exactly one way.
2. Some numbers below 59 cannot be produced in this way at all, while some can be produced in one way and others in more than one way as sums of nonnegative integral multiples of A and B.
3. All numbers above 59 can be produced in more than one way as sums of nonnegative integral multiples of A and B.
What two numbers can A and B be?
(In reply to
possible solution by Ady TZIDON)
When this puzzle was in the queue, some folks said that another rule was unnecessary: that some numbers below 59 were impossible to achieve, some had more than one way and some had exactly one way.
This solution would be ruled out by that rule, as all numbers below 59 would have only one way, with zero times 60.
It seems that rule was in fact needed to rule out this as a solution.

Posted by Charlie
on 20110813 17:29:51 