Creating and manipulating expressions and formulae

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 $n+4$?
problem
Factor list

Age

14 to 16

Challenge level

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
problem
Price match

Age

7 to 11

Challenge level

Can you find pairs of differently sized windows that cost the same?
problem
Finding 3D stacks

Age

7 to 11

Challenge level

Can you find a way of counting the spheres in these arrangements?
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
The Number Jumbler

Age

7 to 14

Challenge level

The Number Jumbler can always work out your chosen symbol. Can you work out how?
problem
Diagonal sums

Age

7 to 14

Challenge level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
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
Partitioning revisited

Age

11 to 14

Challenge level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
problem
Multiply the addition square

Age

11 to 14

Challenge level

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?