Track / Stage 4 / 228 of 340 #488 of 2000

Problem 488

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

1. Consider a $2 \times 3$ grid where each entry is one of 0,1 , and 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.
$\left[\begin{array}{lll} 1 & 2 & 0 \\ 2 & 1 & 0 \end{array}\right]$

Your answer

Official solution

Answer:
9
Any two elements in the same row fix the rest of the grid, so $3^{2}=9$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.