2024 AMC 8 Problems/Problem 16
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[hide]Problem 16
Minh enters the numbers through into the cells of a 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 ?
Solution
These are just left here for future conveniency. “We know that if a row/column of numbers has a single multiple of 3, that entire row/column will be divisible by 3. Since there are 27 multiples of 3 from 1 to 81, We need to find a way to place the 54 non-multiples of 3 such that they take up as many entire rows and columns as possible.”