Problem 22 · 2011 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellationcasework
Lina has placed two tiles on a square game board. Which one of the 5 counters shown (A–E) can she add, so that none of the remaining four counters can be placed anymore?
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Answer: D
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Hint 1 of 2
A good blocking piece should break up the empty area into spaces too small for the others.
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Hint 2 of 2
Place each option and ask: can any other counter still be added?
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Approach: find the counter that blocks every spot for the remaining four
- Two tiles are already placed; adding one more counter should leave no room for any of the other shapes.
- Test each candidate counter and check whether the empty cells can still hold any remaining piece.
- Only counter D fills the board so that none of the other four counters fit anymore.
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