Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Follow the clues to find the mystery number.
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
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?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
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?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
Investigate the different ways you could split up these rooms so that you have double the number.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
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!
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
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?
A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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.
Can you make square numbers by adding two prime numbers together?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
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?
Can you substitute numbers for the letters in these sums?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Can you use the information to find out which cards I have used?
An investigation that gives you the opportunity to make and justify predictions.
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?
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.
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!
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
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?