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

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.

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

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

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

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?

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

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

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

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

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.

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?

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

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

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

A few extra challenges set by some young NRICH members.

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. . . .

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?

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?

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

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

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.

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

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

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.

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

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?

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

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

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. . . .

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 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.

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?

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

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?

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

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

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...

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.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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

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

Use the differences to find the solution to this Sudoku.

Two sudokus in one. Challenge yourself to make the necessary connections.

How many different triangles can you make on a circular pegboard that has nine pegs?