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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Follow the clues to find the mystery number.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Number problems at primary level that require careful consideration.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you find the chosen number from the grid using the clues?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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.
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.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Can you substitute numbers for the letters in these sums?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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.
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?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
What is the best way to shunt these carriages so that each train can continue its journey?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
What could the half time scores have been in these Olympic hockey matches?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
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?
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.
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.