Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge extends the Plants investigation so now four or more children are involved.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A challenging activity focusing on finding all possible ways of stacking rods.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?
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 few extra challenges set by some young NRICH members.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
How many different triangles can you make on a circular pegboard that has nine pegs?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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....?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Can you find all the different triangles on these peg boards, and find their angles?
Can you find all the different ways of lining up these Cuisenaire rods?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
Find out what a "fault-free" rectangle is and try to make some of your own.
You need to find the values of the stars before you can apply normal Sudoku rules.
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?