Problem 20 · 2025 Math Kangaroo
Stretch
Spatial & Visual Reasoning
tiling-tessellationgrid
Joanna divides the figure into five equal-sized, same-shaped parts, each of which consists of three squares. Which of the letters is in the part with the star?
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Answer: E — E
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Hint 1 of 2
All five pieces are the same shape made of three squares, so figure out that shape first from a corner that can only be filled one way.
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Hint 2 of 2
Once you know the piece shape, build outward and watch which three squares end up grouped with the star.
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Approach: find the repeating 3-square piece, then read off the star’s group
- Since every piece is the same three-square shape, start at a corner of the figure where only one shape can fit; that fixes what the repeating piece looks like.
- Lay that same piece again and again to tile the whole figure with no gaps or overlaps — there is only one way it all fits together.
- The piece that ends up covering the starred square also covers the square labelled E, so the answer is (E).
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