How many different symmetrical shapes can you make by shading triangles or squares?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
A challenging activity focusing on finding all possible ways of stacking rods.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A Sudoku based on clues that give the differences between adjacent cells.
Two sudokus in one. Challenge yourself to make the necessary
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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 second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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?
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.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A Sudoku that uses transformations as supporting clues.
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Given the products of diagonally opposite 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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A Sudoku with clues as ratios.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A Sudoku with a twist.
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.
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Use the differences to find the solution to this Sudoku.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one