Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Number problems at primary level that may require resilience.

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.

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

Here is a chance to play a version of the classic Countdown Game.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

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?

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level to work on with others.

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Find a great variety of ways of asking questions which make 8.

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Got It game for an adult and child. How can you play so that you know you will always win?

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?

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

What is the sum of all the digits in all the integers from one to one million?

Investigate the different distances of these car journeys and find out how long they take.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Can you explain the strategy for winning this game with any target?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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?