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Königsberg

Age 11 to 14
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Legend has it that the 'gentlefolk' of Königsberg would spend their Sunday afternoons walking around the town. It is believed they were attempting to 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 their steps.

You might find it easier to study a more diagrammatic representation below (green dots represent the land to the north and south of the river and blue dots the two islands):

Can you succeed where the people of Königsberg failed, and solve the problem of the seven bridges? If not, can you explain why not? If you can, explain how you know that you have all the solutions?


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Calendar Capers

Choose any three by three square of dates on a calendar page...

Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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