MathDB

Given an

m \times n

table consisting of

mn

unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given three colors. Alice wins if there is a figure, such as the ones below, having three different colors. Otherwise Bob is the winner. Determine the winner for all cases of

m

and

n

where

m, n \ge 3

.
Proposed by Toghrul Abbasov, Azerbaijan

Problem Statement