What are the smallest positive integers A, B, C, and D such that A+A > A+B > A+C > B+B > B+C > A+D > C+C > B+D > C+D > D+D ?

Note: Of all solutions, choose the one with the smallest A, then smallest B if there are more than one with the smallest A, etc.

We can easily see that A>B>C>D. This satisfies a lot of the other inequalities. What's left is:

A+C>2B
2B>A+D
B+C>A+D
A+D>2C
2C>B+D

So we have 6 inequalities to satisfy. From a first look, it A, B, C, D cannot be consecutive. Maybe I'll try it later when I have more time.

Posted by np_rt on 2004-11-06 13:17:27