Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Can you find ways to put numbers in the overlaps so the rings have equal totals?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

How many ways can you find to put in operation signs (+ - x รท) to make 100?

By selecting digits for an addition grid, what targets can you make?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you do a little mathematical detective work to figure out which number has been wiped out?

What happens when you add a three digit number to its reverse?

The clues for this Sudoku are the product of the numbers in adjacent squares.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Use the differences to find the solution to this Sudoku.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you make sense of the three methods to work out the area of the kite in the square?

Use your skill and judgement to match the sets of random data.

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

A game in which players take it in turns to choose a number. Can you block your opponent?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?