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

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

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

You have 5 darts and your target score is 44. How many different ways could you score 44?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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!

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?

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

The pages of my calendar have got mixed up. Can you sort them out?

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

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

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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.

What happens when you round these numbers to the nearest whole number?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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!

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?

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?

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?