MathDB

2018 Combinatorics #1

Source:

February 12, 2018

Problem Statement

Consider a

2\times 3

grid where each entry is either

0

1

, or

2

. For how many such grids is the sum of the numbers in every row and in every column a multiple of

3

? One valid grid is shown below:

\begin{bmatrix} 1 & 2 & 0 \\ 2 & 1 & 0 \end{bmatrix}