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This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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This challenge extends the Plants investigation so now four or more children are involved.

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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

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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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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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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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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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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Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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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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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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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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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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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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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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Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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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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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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Can you substitute numbers for the letters in these sums?

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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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Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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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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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.

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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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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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A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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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?

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Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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Investigate what happens when you add house numbers along a street in different ways.

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

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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?