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jmc

counting and probability junior

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 x grid attacks all other squares, as shown below. Suppose a white king and a black king are placed on different squares of a x grid so that they do not attack each other (in other words, not right next to each other). In how many ways can this be done?
problem
(A)
(B)
(C)
(D)
(E)
Solution
If you place a king in any of the corners, they will have spots to go and there are corners, so . If you place a king in any of the edges, they will have spots to go and there are edges so, . That gives us spots to go into totally. So is the answer.
Final answer
E