https://www.facebook.com/hackercup/problems.php?round=544142832342014

https://www.facebook.com/notes/facebook-hacker-cup/2014-round-2-solutions/787413617941208

https://www.facebook.com/notes/facebook-hacker-cup/holdem-numbers-proof-of-monotonicity/787418921274011
For math prove, when a + b + 1 = c + d, there should be only 3 possibilities:
1. a = c & b + 1 = d - replace all d to b
2. a + 1 = c & b = d - replace all c to a
3. a < c < d < b - replace x->x-1 for a<x<=c, x->x+1 for d<=x<b, since (c - a) = (b - d) + 1, every time there's an increase, there should be a decrease

It can never be that c < a