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'Shunting Puzzle' printed from https://nrich.maths.org/

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Why do this problem?

This problem is not for the faint hearted! It requires logical thinking and perseverance. Learners who enjoyed this problem may like to try Single Track .

Key questions

How could you start?
How will you remember what you have tried?
Remember that the engine can push and pull.
Perhaps using some counters will help?