Problem 12 · 2015 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracing
The side lengths of each of the small squares in the diagram are 1. How long is the shortest path from “Start” to “Ziel”, if you are only allowed to move along the sides and the diagonals of the squares?
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Answer: C — \(2+2\sqrt{2}\)
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Hint 1 of 2
You may step along square sides (length 1) or square diagonals (length √2); mix them to go down and across.
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Hint 2 of 2
Two diagonal steps drop you down a row and across, then walk straight; compare 2√2 + 2 with the others.
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Approach: combine diagonals and straight edges
- From Start, two diagonal moves (each √2) carry you down one row and two columns across: 2√2.
- Then walk straight along the bottom edge the remaining distance: 2 unit sides = 2.
- Total shortest length = 2 + 2√2.
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