Problem 15 · 2022 Math Kangaroo
Hard
Logic & Word Problems
casework
Four circles joined by a line form a chain of four. The numbers 1, 2, 3 and 4 each appear exactly once in every row, every column and every chain of four. Which number goes in the circle with the question mark?
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Answer: B — 2
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Hint 1 of 2
The rule is like a small Latin square: 1, 2, 3, 4 each appear once per row, per column and per chain.
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Hint 2 of 2
Use the given numbers and these no-repeat rules to pin down the ? cell.
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Approach: apply the row, column and chain constraints
- Each row, each column and each chain of four must contain 1, 2, 3, 4 exactly once.
- Filling in forced cells from the given 3, 2, 2, 1 narrows the options.
- The question-mark circle is forced to be 2.
- So the answer is B.
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