Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
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?
Investigate the different distances of these car journeys and find out how long they take.
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
Can you make square numbers by adding two prime numbers together?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
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?
What is happening at each box in these machines?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
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?
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?
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?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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!
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Are these domino games fair? Can you explain why or why not?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.