MathDB

Let

n

be a positive integer. Dominoes are placed on a

2n \times 2n

board in such a way that every cell of the board is adjacent to exactly one cell covered by a domino. For each

n

, determine the largest number of dominoes that can be placed in this way. (A domino is a tile of size

2 \times 1

1 \times 2

. Dominoes are placed on the board in such a way that each domino covers exactly two cells of the board, and dominoes do not overlap. Two cells are said to be adjacent if they are different and share a common side.)

Problem Statement