Problem 30 · 2011 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardcareful-counting
Mark plays a computer game on a 4×4 board. The cells each have a colour which is initially hidden. If he clicks on a cell it turns red or blue. He knows that there are exactly two blue cells and that they share one side. What is the smallest number of clicks with which he can definitely find the blue cells?
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Answer: B — 10
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Hint 1 of 2
Think of the two blue cells as a domino placed somewhere on the board.
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Hint 2 of 2
You need a clicking pattern that cannot miss the domino in any position — count the minimum needed.
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Approach: find the fewest clicks that always reveal the two adjacent blue cells
- The two blue cells share an edge, so they form a domino somewhere in the 4×4 grid.
- A clever set of clicks must hit at least one blue cell no matter where that domino lies, then confirm its partner.
- The smallest number of clicks that guarantees finding both is 10.
Mark:
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