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Only Connect

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

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Ding Dong Bell

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

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Königsberg

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

Pattern of Islands

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Picture of islands

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island and so that:

  • three of the islands have three bridges leading from them;
  • two have two bridges leading from them;
  • and one island has only one bridge leading from it?