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There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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Can you substitute numbers for the letters in these sums?

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Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

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Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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Use the information to work out how many gifts there are in each pile.

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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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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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Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

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

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Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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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?

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Can you score 100 by throwing rings on this board? Is there more than way to do it?

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On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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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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This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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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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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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

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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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Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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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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Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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Number problems at primary level that may require resilience.

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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 out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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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?

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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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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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Number problems at primary level that require careful consideration.

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On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

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Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

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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?

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

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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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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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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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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?