Find the number of non-decreasing sequences of 75 integers from 1 to 75 which have same mean as the median.
For all sequences of 75 from 1,1,1...1,1,1 to 75,75,75...75,75,75 -- the 38th term will be the median. This term can take all of the integer values from 1 to 75. The mean is the average of all 75 terms (including the median). To be counted, the sum of all 75 must be divisible by 75, since the median is an integer. If one is really going to try to solve this (I decline), we could start with the two extremes given above, and any of the 73 others with identical terms. Then? Good Luck! or a BIG envelope.