Problem 16 · 2019 Math Kangaroo
Hard
Spatial & Visual Reasoning
tiling-tessellationcasework
A 3 × 2 rectangle can be covered in two ways by two of the L-shaped figures, as shown. In how many ways can the diagram on the right be covered by these L-shaped figures?
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Answer: B — 2
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Hint 1 of 2
The two L-pieces must pair up the way they did in the 3 × 2 box.
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Hint 2 of 2
Find a corner cell that only one piece can reach, and let that placement force the rest.
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Approach: let a forced corner pin down the whole covering
- Look at a corner cell of the figure: only one orientation of an L-piece can cover it while staying inside.
- Once that corner piece is placed, the cells it leaves can be completed by the remaining pieces in just two consistent ways.
- So the figure can be covered in exactly 2 ways.
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