Latin multiplication
Can you choose one number from each row and column in this grid to form the largest possibe product?
Age
11 to 14
Challenge level
Problem
Image
I choose three numbers from this number square, including one number from each row and one number from each column. I then multiply the three numbers together. What is the largest possible product?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
We consider the different possible choices from the top row.
If $1$ is chosen then we can either choose $1$,$5$,$9$ or $1$,$6$,$8$ giving products of $45$ and $48$ repectively.
If $2$ is chosen then we can either choose $2$,$4$,$9$ or $2$,$7$,$6$ giving products of $72$ and $84$ repectively.
If $3$ is chosen then we can either choose $3$,$4$,$8$ or $3$,$7$,$5$ giving products of $96$ and $105$ repectively.
So $105$ is the largest possible product.