Problem 13 · 2014 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationcomposition
Erwin has the four paper pieces shown. He has to cover a special shape exactly with these four pieces. In which drawing can he do this, when the one piece is placed as shown? (Choose the matching picture.)
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Answer: C
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Hint 1 of 3
The piece that is already placed covers part of the shape, so look at the empty gap that is left.
Still stuck? Show hint 2 →
Hint 2 of 3
Ask whether the other three pieces can fill that gap with no holes and no sticking out.
Still stuck? Show hint 3 →
Hint 3 of 3
Try each drawing and keep the only one that the pieces fit perfectly.
Show solution
Approach: see which outline the leftover three pieces fill exactly
- Once the shown piece is set down, the empty space that remains has a fixed shape.
- Imagine sliding the other three pieces in like a little jigsaw, covering every square with no gaps and no overlaps.
- Only one of the drawings lets all four pieces fit exactly.
- That drawing is C.
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