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Lastly - Well

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

Counting Factors

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

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?

Not a Polite Question

Age 11 to 14 Challenge Level:

When asked how old she was, the teacher replied:

My age in years is not prime but odd
and when reversed and added to my age
you have a perfect square.

Or you can reverse and subtract, and
again you have a perfect square.

Divisibility. Properties of numbers. Other equations. Diophantine equations. Creating and manipulating expressions and formulae. Simultaneous equations. Working systematically. Place value. Integers. Factors and multiples.