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AMO 2016 Grade 3 Question 15

AMO · AMO 2016 Grade 3

Question 15

In the figure shown, the numbers 1, 2, 3, 5, 6, and 7 are to be placed one in each empty square. The following 4 sums are the same: the numbers in the left column, the numbers in the right column, and the numbers in each diagonal. What is the greatest possible product of the 3 numbers across the grey row?

Question illustration