Problem 17 · 2023 Math Kangaroo
Hard
Logic & Word Problems
periodic-patterncareful-counting
An underground line has the six stations A, B, C, D, E and F. The train stops at every station. After reaching the end of the line (A or F) the train continues in the opposite direction. The train conductor starts his journey in station B. His first stop is in station C. In which station will be his 46th stop?
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Answer: D — D
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Hint 1 of 2
List the stops in order; the train bounces off the ends A and F.
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Hint 2 of 2
The sequence of stops repeats, so find the cycle length and use the remainder.
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Approach: list the bouncing sequence, find its period, take 46 mod period
- Starting at B and first stopping at C, the stops run C,D,E,F,E,D,C,B,A,B and then repeat with period 10.
- Since 46 = 4×10 + 6, the 46th stop matches the 6th stop in the cycle.
- The 6th stop is D.
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