Problem 30 · 2019 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcaseworkmagic-square
Numbers are placed in the square grid shown so that each of 1, 2, 3, 4 and 5 appears exactly once in every row and in every column. In addition, the sum of all the numbers in each of the three black-bordered sections must be the same. Which number must be written in the top right cell?
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Answer: C — 3
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Hint 1 of 2
It is a 5×5 Latin square (1–5 once per row and column) split into three black-bordered regions of equal sum.
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Hint 2 of 2
All 25 cells sum to 75, so each region sums to 25; combine that with the given 2 and the row/column rules to force the top-right cell.
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Approach: use the equal region sums of 25 with the Latin-square rules
- Each row contains 1–5 and sums to 15, so the whole grid sums to 75.
- The three black-bordered regions have equal sums, so each region sums to \(75 \div 3 = 25\).
- Tracking the cells in each region together with the placed 2 and the once-per-row/column constraint forces the entries step by step.
- The top right cell is pinned to 3 — answer (C).
Mark:
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