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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

How many ways can you arrange the bridges if the island with one bridge joins to the island with two bridges to the second island with two bridges (1-2-2)?

 

Now extend this systematic approach by altering one of the constraints (say 1-2-3).