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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?

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Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

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In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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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?

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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?

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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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Number problems at primary level that require careful consideration.

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

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

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Can you substitute numbers for the letters in these sums?

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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?

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

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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?

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Can you use this information to work out Charlie's house number?

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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?

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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?

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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?

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This dice train has been made using specific rules. How many different trains can you make?

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

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Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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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.

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Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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The Zargoes use almost the same alphabet as English. What does this birthday message say?

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What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

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Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

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

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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?

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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!

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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?

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There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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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?

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Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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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.

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Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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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?

Challenge Level

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!