MathDB

Let

k

and

n

be integers such that

k\ge 2

and

k \le n \le 2k-1

. Place rectangular tiles, each of size

1 \times k

, or

k \times 1

on a

n \times n

chessboard so that each tile covers exactly

k

cells and no two tiles overlap. Do this until no further tile can be placed in this way. For each such

k

and

n

, determine the minimum number of tiles that such an arrangement may contain.

Problem Statement