Creating and manipulating expressions and formulae

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

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

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

After performing some operations, what number is your answer always a multiple of?

Can you find the value of t in these equations?

Can you find a rule which connects consecutive triangular numbers?

Can you work out the value of x in this 'power-full' equation?

Each letter stands for a different digit, and S is non-zero. Which letter has the lowest value?

Derive an equation which describes satellite dynamics.

What does the sum of these three numbers tell us about their product?