Question

Show that there must be atleast 91 choices to choose 6 integers from 1 to 15 so all have the same sum

Answer 1

There are 6C15 = 5005 ways to choose 6 numbers

The minimum sum is 1+2+2+4+5+6 = 21

the maximum sum is 10+11+12+13+14+15 = 75

Thus there are only 55 different sums possible

5005/55 = 91

So, at least one of the sums must appear at least 91 times.