Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you find the chosen number from the grid using the clues?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

What two-digit numbers can you make with these two dice? What can't you make?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

What happens when you round these three-digit numbers to the nearest 100?

Can you replace the letters with numbers? Is there only one solution in each case?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Can you make square numbers by adding two prime numbers together?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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.

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

What could the half time scores have been in these Olympic hockey matches?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Using the statements, can you work out how many of each type of rabbit there are in these pens?