MathDB

Given are two positive integers

k

and

n

with

k \le n \le 2k - 1

. Julian has a large stack of rectangular

k \times 1

tiles. Merlin calls a positive integer

m

and receives

m

tiles from Julian to place on an

n \times n

board. Julian first writes on every tile whether it should be a horizontal or a vertical tile. Tiles may be used the board should not overlap or protrude. What is the largest number

m

that Merlin can call if he wants to make sure that he has all tiles according to the rule of Julian can put on the plate?

Problem Statement