Problem 15 · 2016 Math Kangaroo
Medium
Logic & Word Problems
casework
Chantal has placed numbers in two of the nine cells (see diagram). She wants to place the numbers 1, 2, 3 in every row and every column exactly once. What is the sum of the two numbers in the grey cells?
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Answer: C — 4
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Hint 1 of 2
Each row and each column must hold 1, 2, 3 exactly once, like a tiny Sudoku.
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Hint 2 of 2
Fill in the forced cells from the given 1 and 2, then read the two grey cells.
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Approach: fill the 3×3 Latin square from the given clues
- The top-left is 1 and the centre is 2; the grey cells are the middle and bottom of the right column.
- The top row must finish 1, 3, 2, so the top-right cell is 2.
- The right column then needs 1 and 3 in its grey cells, so their sum is 1 + 3 = 4.
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