Problem 4 · 2013 Math Kangaroo
Easy
Spatial & Visual Reasoning
Counting & Probability
tiling-tessellationspatial-reasoningcareful-counting
Melanie has a square piece of paper with a 4×4 grid drawn on it. She cuts along the gridlines, cutting out several shapes that each look like the one pictured or its mirror image. How many squares are left over if she cuts out as many shapes as possible?
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Answer: C — 4
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Hint 1 of 2
The shape is a 4-square piece; the grid holds 16 squares in total.
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Hint 2 of 2
Try to fit as many copies (or mirror images) as you can without overlap, then count the leftovers.
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Approach: tile and count leftovers
- The 4×4 grid has 16 unit squares; each cut-out piece uses 4 of them.
- These S/Z-shaped pieces cannot fill the 4×4 square completely.
- The best packing fits 3 pieces (12 squares), leaving 4 squares uncovered.
- So 4 squares are left over.
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