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### Number and algebra

### Geometry and measure

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### Working mathematically

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### Consecutive Numbers

### Adding All Nine

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Age 11 to 14

Challenge Level

- Problem
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There are exactly 3 ways to add 4 odd numbers to get 10. Re-arranging the order of the numbers does not give a new solution. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?

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!