Given the products of adjacent cells, can you complete this Sudoku?
Find out about Magic Squares in this article written for students. Why are they magic?!
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Can you find the chosen number from the grid using the clues?
Follow the clues to find the mystery number.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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!
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Can you substitute numbers for the letters in these sums?
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?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Can you work out some different ways to balance this equation?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Number problems at primary level that require careful consideration.
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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.