How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Use the clues about the symmetrical properties of these letters to place them on the grid.

A challenging activity focusing on finding all possible ways of stacking rods.

How many different symmetrical shapes can you make by shading triangles or squares?

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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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

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?

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

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.

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

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?

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

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

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

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?

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.

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

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?

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

A few extra challenges set by some young NRICH members.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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. . . .

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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.

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

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

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. . . .

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Four small numbers give the clue to the contents of the four surrounding cells.

In how many ways can you stack these rods, following the rules?

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

An activity making various patterns with 2 x 1 rectangular tiles.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

Use the differences to find the solution to this Sudoku.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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.