"Attacking" combo
Source: 2024 AMC 8 #17
October 11, 2024
AMC 82024 AMC 8AMC
Problem Statement
A chess king is said to ''attack'' all squares one step away from it (basically any square right next to it in any direction), horizontally, vertically, or diagonally. For instance, a king on the center square of a 3 x 3 grid attacks all 8 other squares, as shown below. Suppose a white king and a black king are placed on different squares of 3 x 3 grid so that they do not attack each other. In how many ways can this be done?[asy]
/* AMC8 P17 2024, revised by Teacher David */
unitsize(29pt);
import math;
add(grid(3,3));pair [] a = {(0.5,0.5), (0.5, 1.5), (0.5, 2.5), (1.5, 2.5), (2.5,2.5), (2.5,1.5), (2.5,0.5), (1.5,0.5)};for (int i=0; ilabel("", (1.5,1.5));
[/asy]