Powers and roots

problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
In between

Age

16 to 18

Challenge level

Can you find the solution to this algebraic inequality?
problem
Lastly - well

Age

11 to 14

Challenge level

What are the last two digits of 2^(2^2003)?
problem
What an odd fact(or)

Age

11 to 14

Challenge level

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

Age

16 to 18

Challenge level

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
problem
Sept 03

Age

11 to 14

Challenge level

What is the last digit of the number 1 / 5^903 ?
problem
Cubes within cubes

Age

7 to 14

Challenge level

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
problem
Largest number

Age

11 to 14

Challenge level

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
problem
The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
problem
Number rules - OK

Age

14 to 16

Challenge level

Can you produce convincing arguments that a selection of statements about numbers are true?