Problem 24 · 2013 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellationarea
Beatrice has several grey tiles that all look exactly like the one pictured. At least how many of these tiles does she need in order to make a complete square?
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Answer: B — 4
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Hint 1 of 3
Try fitting copies of the tile together so they make a big square with no gaps and no overlaps.
Still stuck? Show hint 2 →
Hint 2 of 3
Turn and rotate the copies so their stair-step edges lock into each other.
Still stuck? Show hint 3 →
Hint 3 of 3
Start small: see whether 2 or 3 copies can ever make a square before trying 4.
Show solution
Approach: rotate copies of the tile so they lock into a square, using as few as possible
- Slide and rotate copies of the tile so their jagged edges fit together with no gaps.
- Two or three copies cannot close up into a full square, but four copies do fit together into one.
- So the fewest she needs is 4 tiles, which is answer B.
Mark:
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