Problem 5 · 2015 Math Kangaroo
Easy
Spatial & Visual Reasoning
spatial-reasoningcareful-counting
Florian has 10 equally long metal strips with equally many holes. He bolts the metal strips together in pairs. Now he has five long strips (see the diagram). Which of the long strips is the shortest?
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Answer: B
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Hint 1 of 2
Each long strip is two of the equal short strips bolted together, but they overlap by some holes.
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Hint 2 of 2
The strip that overlaps the most (shares the most holes) ends up the shortest.
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Approach: more overlap means a shorter combined strip
- All the short strips are the same length, so the total length of a pair depends only on how much the two pieces overlap.
- The more holes the two pieces share, the shorter the finished strip.
- Strip B has the biggest overlap, so it is the shortest: choice B.
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