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.

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?

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.

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?

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. . . .

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

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

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?"

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.

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?

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 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?

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

A few extra challenges set by some young NRICH members.

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

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 many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

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

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

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

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

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?

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

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?

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?

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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?

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?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?