Creating and manipulating expressions and formulae

problem
Operating machines

Age

16 to 18

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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?
problem
Carry over

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?
problem
Unusual long division - square roots before calculators

Age

14 to 16

Challenge level

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

Age

14 to 18

Challenge level

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?
problem
Interactive number patterns

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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 $n+4$?