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?

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?

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

Try this matching game which will help you recognise different ways of saying the same time interval.

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?

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?

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

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?

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

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

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?

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?

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

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

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?

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.

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

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?

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

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 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?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

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

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.

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

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?

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?

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?

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

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?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

Number problems at primary level that require careful consideration.

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

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

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

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....?

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?

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.