MathDB
Annoying Products

Source: 2024 AMC8 P16

January 25, 2024
AMCAMC 82024 AMC 8

Problem Statement

Minh enters the numbers from 1 to 81 in a 9×99\times9 grid in some order. She calculates the product of the numbers in each row and column. What is the least number of rows and columns that could have a product divisible by 3?
<spanclass=latexbold>(A)</span>8<spanclass=latexbold>(B)</span>9<spanclass=latexbold>(C)</span>10<spanclass=latexbold>(D)</span>11<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>8\qquad<span class='latex-bold'>(B) </span>9\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>11\qquad<span class='latex-bold'>(E) </span>12