Problem:
Let be distinct integers from to . The minimum possible positive value of
can be written as , where and are relatively prime positive integers. Find .
Solution:
To minimize the value of the expression , we first aim to make the numerator as small as possible. The smallest positive value it can take is , so we try to find integers such that .
Trying small combinations, we find that and satisfy the condition. These six integers are distinct and between and , so they are valid.
This leaves us with the remaining three digits: , , and , which we assign to , , and . Then .
Thus, the value becomes .
If instead the numerator were greater than , say or more, then the smallest possible value of the expression would be at least .
Hence, the minimum possible positive value is , and the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions