Problem 17 · 2021 Math Kangaroo
Hard
Algebra & Patterns
sum-constraint
In the \(5 \times 5\) square shown the sum of the numbers in each row and in each column is the same. There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?
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Answer: B — 10
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Hint 1 of 2
The grand total of a 1–25 square fixes the common row/column sum.
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Hint 2 of 2
Use row and column equations through the marked cell to pin its value.
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Approach: use the magic sum, then solve the right cells
- The numbers 1–25 total 325, so each row and column sums to 65.
- Solving the equations for row 2 and the involved columns forces the entries 7, 15, 13, 17 around column 4.
- Column 4 then gives 22 + e + 1 + j + ? = 65 with e=15, j=17, so ? = 10.
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