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What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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Repeaters

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.

Legs Eleven

Age 11 to 14 Challenge Level:


Imagine starting with the number $5238$.

We can write it as
                                  $5000+200+30+8$
or 
                                  $5\times1000 + 2\times100 + 3\times10 + 8\times1$

Can you express the second number in the same way?

How many 5s, 2s, 3s and 8s are there when you combine the two numbers?