Creating and manipulating expressions and formulae

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

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

Can you work out Ali's age based on the diagram?

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

How good are you at finding the formula for a number pattern ?

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?