Maths Olympiad Prep

Track / Stage 4 / 276 of 340 #536 of 1964

Problem 536

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer

1. [3] Joe B. first places the black king in one corner of the board. In how many of the 35 remaining squares can he place a white bishop so that it does not check the black king?

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Answer: 30 Any square not on the diagonal containing the corner is a possible location, and there are 366=3036-6=30 such squares.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.