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Can you substitute numbers for the letters in these sums?

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

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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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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.

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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?

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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?

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

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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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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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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?

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Number problems at primary level that require careful consideration.

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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 group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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

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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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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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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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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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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?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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

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Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

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There are lots of different methods to find out what the shapes are worth - how many can you find?

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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

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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!

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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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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?

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What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

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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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The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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

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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?

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

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

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

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

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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?

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

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