Track / Stage 4 / 288 of 340 #548 of 1964

Problem 548

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer

[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?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Answer: 30 Any square not on the diagonal containing the corner is a possible location, and there are $36-6=30$ such squares.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.