Case 1: Kangaroos are placed diagonally.
There's only one way to place them in this manner.
Case 2: Two kangaroos are in one row/column, and the third kangaroo is in a different row/column.
There are 3 × 2 = 6 ways to choose the row/column for the lone kangaroo, and for each choice, there are 2 × 2 = 4 ways to place the other two kangaroos. However, this counts each configuration twice (once for each kangaroo in the pair), so we divide by 2. Therefore, there are 6 × 4 / 2 = 12 ways for this case.
Total number of ways = 1 + 12 = 13
So, there are 13 ways to place three kangaroos in three different cells in a 3 by 3 grid such that they are not adjacent horizontally or vertically to each other.
