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Lastly - Well

What are the last two digits of 2^(2^2003)?

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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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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?

Thirty Six Exactly

Age 11 to 14 Challenge Level:

The number $12 = 2^2 \times 3$ has 6 factors. What is the smallest natural number with exactly 36 factors?