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What an Odd Fact(or)
Age 11 to 14
Challenge Level 
What can you say about the patterns in the last digits of powers of $2$, $3$, $4$ etc?
How can you use these patterns to say what the last digits are of the numbers raised to the power $99$?
Now can you say whether the sum is divisible by $5$?
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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.