Problem 8 · 2010 Math Kangaroo
Easy
Logic & Word Problems
casework
Brigitte goes on holiday to Verona and plans to cross all five of the famous old bridges over the Etsch (Adige) at least once. She starts at the train station and when she returns there she has crossed each of the five bridges but no others. During her walk she has crossed the river n times. What is a possible value for n?
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Answer: D — 6
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Hint 1 of 2
Each bridge she crosses takes her from one bank to the other, so think about which side she ends up on.
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Hint 2 of 2
Since she returns to the starting bank, the number of crossings must be even.
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Approach: parity of river crossings on a closed route
- Every bridge she walks over flips her from one bank to the other, so the river crossing count must be even for her to come back to the station's bank.
- That rules out the odd choices 3, 5 and 7, and 4 is too few to cover all five bridges.
- Crossing the five bridges with one used twice gives 6 crossings, which works.
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