Creating and manipulating expressions and formulae

problem
Painted cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
problem
Your number is...

Age

7 to 14

Challenge level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
problem
Perfectly square

Age

14 to 16

Challenge level

The sums of the squares of three related numbers is also a perfect square - can you explain why?
problem
More number pyramids

Age

11 to 14

Challenge level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
problem
Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Circles in circles

Age

16 to 18

Challenge level

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.
problem
Special numbers

Age

11 to 14

Challenge level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
problem
Poly fibs

Age

16 to 18

Challenge level

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
problem
Fibonacci factors

Age

16 to 18

Challenge level

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
problem
Chocolate 2010

Age

14 to 16

Challenge level

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...