A new December and a new bunch of puzzles from mscroggs.co.uk.

Out of the 11 available integers, 5 is the 5th, with 4 integers before it and 6 after. A set of integers is well formed, if 5 is the middle integer, with n integers before it and n after.

n = 0, 1 way to do that.

n = 1, 4 choices in front, 6 choices after, 4*6 = 24 ways to do that.

n = 2, (4 c 2) choices in front, (6 c 2) choices after, (4 c 2) * (6 c 2) = 4*3/2 * 6*5/2 = 6*15 = 90 ways to do that.

n = 3, (4 c 3) choices in front, (6 c 3) choices after, (4 c 3) * (6 * 3) = 4 * 6*5*4/(3*2) = 4*20 = 80 ways to do that.

n = 4, 1 choice in front, (6 c 4) choices after, 6*5/2 = 15 ways to do that.

1+24+90+80+15 = 210.