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Ratty
Age 11 to 14
Challenge Level 
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? Explain your reasoning. Draw some diagrams of your own and mark in these angles. If in addition you know that the lines $AB$ and $CD$ are parallel which angles can you find?
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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?