Problem 17 · 2012 Math Kangaroo
Stretch
Logic & Word Problems
casework
In an arithmetic-sudoku, the values 1, 2, 3, 4 each appear exactly once in every row and every column. (First work out the value written in each cell.) Which value belongs in the grey square?
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Answer: C — 3
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Hint 1 of 2
First work out the number in each cell from its little sum, then it is a 4-by-4 Latin square.
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Hint 2 of 2
Each row and column holds 1, 2, 3, 4 once; fill the forced cells until you reach the grey one.
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Approach: work out each little sum, then solve like a tiny sudoku
- First do the small sums in the cells, for example \(6-3=3\), \(4-1=3\), \(1+3=4\), \(8-7=1\), \(9-7=2\), \(2-1=1\), so each cell becomes a single number.
- Now it is a 4-by-4 puzzle where 1, 2, 3, and 4 each appear once in every row and once in every column.
- Filling the rows and columns one forced cell at a time leaves only the number 3 able to go in the grey square.
- The grey square is 3.
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