Problem 19 · 2018 Math Kangaroo
Medium
Arithmetic & Operations
sum-constraint
Jakob writes one of the natural numbers 1 to 9 into each cell of a 3×3 table. Then he works out the sum of the numbers in each row and in each column. Five of his results are 12, 13, 15, 16 and 17. What is the sixth sum?
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Answer: A — 17
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Hint 1 of 2
Add up all nine numbers 1 to 9.
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Hint 2 of 2
The three row sums total that, and so do the three column sums; use the grand total of all six sums.
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Approach: use that rows and columns each total 45
- The numbers 1 to 9 add to 45, so the three row sums total 45 and the three column sums total 45 — all six sums total 90.
- Five of them are 12 + 13 + 15 + 16 + 17 = 73.
- The sixth sum is 90 − 73 = 17.
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