Problem 19 · 2011 Math Kangaroo
Hard
Spatial & Visual Reasoning
tiling-tessellationarea
Daniel wants to make a complete square using pieces only like the one shown. What is the minimum number of pieces he must use?
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Answer: E — 20
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Hint 1 of 2
Each piece covers 5 squares, so the square's area must be a multiple of 5.
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Hint 2 of 2
A 5×5 square cannot be tiled by this L-shape; try the next size that can.
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Approach: size the square so the L-pentomino can tile it
- The piece is an L made of 5 unit squares, so the big square's area must be a multiple of 5.
- A 5-by-5 square can't actually be tiled by this L-shape, but a 10-by-10 square can.
- A 10-by-10 square is 100 squares, needing 100 ÷ 5 = 20 pieces.
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