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Power Crazy
Age 11 to 14
Challenge Level 
What can you say about the values of $n$ that make $7^n+3^n$ a multiple of 10?
Are there other pairs of integers between 1 and 10 which have similar properties?
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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!
