2024 AMC 8 Problems/Problem 17

Revision as of 12:32, 26 January 2024 by Math645 (talk | contribs) (Solution 1)

Problem

A chess king is said to attack all the squares one step away from it, 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 a $3$ x $3$ grid so that they do not attack each other. In how many ways can this be done?

(A) $20$ (B) $24$ (C) $27$ (D) $28$ (E) $32$

==Solution 1== by Math 645

Corners have 5 spots to go and 4 corners so 5*4=20. Sides have 3 spots to go and 4 sides so 3*4=12 20+12=32 in total. E (32) is the answer.

Video Solution 1 by Math-X (First understand the problem!!!)

https://youtu.be/nKTOYne7E6Y

~Math-X

Video Solution 2 (super clear!) by Power Solve

https://youtu.be/SG4PRARL0TY