Problem Statement
Three tokens A, B, C are placed on distinct cells of a 3×3 grid. A is not on the border. B is in a corner. C is not adjacent (edge-sharing) to B. How many distinct placements are possible?
Explanation
A not on border ⇒ A must be center (only non-border cell). B in a corner ⇒ 4 choices. For each B, C cannot be edge-adjacent to B. A occupies center, which is adjacent to all 4 edges but not a corner; adjacency considered is edge-sharing, not diagonal. From a corner, the edge-adjacent cells are two border cells plus the center (but center is taken by A). So C cannot be those two edges; it can be the opposite corner, the other two corners not sharing an edge, and any border cells not adjacent to B. Counting valid C for each corner B gives 3 choices per B. Thus 4×3 = 12.
Code Solution
SolutionRead Only
A at center; for each corner B ⇒ 3 valid C ⇒ 12
Practice Sets
This question appears in the following practice sets:
