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?
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku that uses transformations as supporting clues.
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku based on clues that give the differences between adjacent cells.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
A Sudoku with a twist.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A Sudoku with clues as ratios.
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
A Sudoku with clues as ratios or fractions.
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
A Sudoku with clues given as sums of entries.
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?
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A pair of Sudoku puzzles that together lead to a complete solution.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
A challenging activity focusing on finding all possible ways of stacking rods.
Four small numbers give the clue to the contents of the four
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.