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 in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

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.

A few extra challenges set by some young NRICH members.

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?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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.

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. . . .

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.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some 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?

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?"

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?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Given the products of adjacent cells, can you complete this Sudoku?

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. . . .

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Find out what a "fault-free" rectangle is and try to make some of your own.

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.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Can you find all the ways to get 15 at the top of this triangle of numbers?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?