HMMT 十一月 2008 · GEN2 赛 · 第 2 题

HMMT November 2008 — GEN2 Round — Problem 2

[ 4 ] Joe B. then places a white king in the opposite corner of the board. How many total ways can he place one black bishop and one white bishop so that neither checks the king of the opposite color?

解析

[ 4 ] Joe B. then places a white king in the opposite corner of the board. How many total ways can he place one black bishop and one white bishop so that neither checks the king of the opposite color? Answer: 876 Observe that either both bishops are on the diagonal containing both kings or neither ( ) 4 are. If both are on the diagonal, each of the = 6 choices of pairs of squares yields one possible 2 configuration, so there are 6 possibilities in this case. Off the diagonal, any pair of locations works, giving 30 · 29 = 870 possibilities in this case. Summing, we obtain 870 + 6 = 876 total possibilities.