2017 AIME I Problems/Problem 11
We know that if is a median, then will be the median of the medians.
WLOG, assume is in the upper left corner. One of the two other values in the top row needs to be below , and the other needs to be above . This can be done in ways. The other can be arranged in ways. Finally, accounting for when is in every other space, our answer is . But we only need the last digits, so is our answer.
~Solution by SuperSaiyanOver9000, mathics42