Problems(1)
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("K", (1.5,1.5));
[/asy]<spanclass=′latex−bold′>(A)</span> 20<spanclass=′latex−bold′>(B)</span> 24<spanclass=′latex−bold′>(C)</span> 27<spanclass=′latex−bold′>(D)</span> 28<spanclass=′latex−bold′>(E)</span> 32
AMC 82024 AMC 8AMC