MathDB

Maker and Breaker are building a wall. Maker has a supply of green cubical building blocks, and Breaker has a supply of red ones, all of the same size. On the ground, a row of

m

squares has been marked in chalk as place-holders. Maker and Breaker now take turns in placing a block either directly on one of these squares, or on top of another block already in place, in such a way that the height of each column never exceeds

n

. Maker places the first block. Maker bets that he can form a green row, i.e. all

m

blocks at a certain height are green. Breaker bets that he can prevent Maker from achieving this. Determine all pairs

(m,n)

of positive integers for which Maker can make sure he wins the bet.

Problem Statement