M is the number of six-element subsets that can be chosen from the set of the first 15 positive integers so that at least three of the six numbers are consecutive.
(In reply to 2 computer solutions; the second is probably right
Printing out all the positional combinations of x's for the chosen numbers shows they are all unique-- all 2155 of them.
It looks as if the 2155 is the right answer, and the 550 of the direct count is undercounting.
Posted by Charlie
on 2016-02-09 16:15:26