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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?
How many solutions can you find?
Can you convince us that you have all of them?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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!