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?

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

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 is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Can you use the information to find out which cards I have used?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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?

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

This challenge is about finding the difference between numbers which have the same tens digit.

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Can you find all the different ways of lining up these Cuisenaire rods?

Number problems at primary level that require careful consideration.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?