Problem 13 · 2020 Math Kangaroo
Hard
Logic & Word Problems
path-tracingwork-backward
Amelia built a crown using 10 copies of the small piece shown. The pieces were joined so that touching sides always show the same number, as in the picture, where four pieces are filled in. What number appears in the coloured triangle?
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Answer: A — 1
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Hint 1 of 3
All ten pieces are exact copies, so the same little numbers repeat as you go around the ring.
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Hint 2 of 3
Where two pieces touch, the touching numbers match, which lines the pieces up the same way each time.
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Hint 3 of 3
Once you know how one piece sits, every piece sits the same, so jump that pattern around to the colored triangle.
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Approach: use the repeating pattern of identical pieces around the ring
- Every piece is the same copy, and because touching sides must show equal numbers, each piece is placed in the very same way as its neighbour.
- So the numbers repeat in the same order all the way around the crown, like a pattern that copies itself ten times.
- Reading that repeating pattern from the filled-in pieces around to the colored triangle, the number landing there is 1, choice A.
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