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?
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.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
You need to find the values of the stars before you can apply normal Sudoku rules.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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 few extra challenges set by some young NRICH members.
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?"
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.
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?
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.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
Given the products of adjacent cells, can you complete this Sudoku?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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?
Can you use the information to find out which cards I have used?
A challenging activity focusing on finding all possible ways of stacking rods.
Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
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.
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!
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.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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.
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?
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?
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?
This dice train has been made using specific rules. How many different trains can you make?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
In this matching game, you have to decide how long different events take.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?