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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!


Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?


Age 11 to 14
Challenge Level

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?