Problem 9 · 2012 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationspatial-reasoning
Anna has made two L-shapes, each out of 4 squares (8 squares in all). How many of the following 4 shapes can she make using both L-shapes?
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Answer: E — 4
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Hint 1 of 2
Each L is made of 4 squares; two of them give 8 squares, so try to cover each shape with two L pieces.
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Hint 2 of 2
Turn and flip the L freely and see which target shapes it can fill.
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Approach: try to tile each shape with two L-pieces
- Each L-piece covers 4 squares, and every shape shown has 8 squares, so a fit is at least possible by area.
- Trying the two L-pieces (rotated or flipped) on each shape, every one of the four can be built.
- So Anna can make all of them.
- The answer is 4.
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