Two squares of an 8 × 8 chessboard are chosen so that they share a common side. In how many ways can this be done?

Question

Accepted Answer

112. In each of the 8 rows there are 7 side-by-side pairs: 8×7=56. The same holds for the 8 columns: 56. Total 56+56=112. (2016 =^64C_2 counts any two squares.)

Two squares of an $8 \times 8$ chessboard are chosen so that they share a common side. In how many ways can this be done?

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Two squares of an 8×8 chessboard are chosen so that they share a common side. In how many ways can this be done?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Permutations & Combinations practice

Two squares of an $8 \times 8$ chessboard are chosen so that they share a common side. In how many ways can this be done?