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?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
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.
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?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku based on clues that give the differences between adjacent cells.
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
This Sudoku combines all four arithmetic operations.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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.
Four small numbers give the clue to the contents of the four
A Sudoku with a twist.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A pair of Sudoku puzzles that together lead to a complete solution.
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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 Sudoku, based on differences. Using the one clue number can you find the solution?
You need to find the values of the stars before you can apply normal Sudoku rules.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
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?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
How many different symmetrical shapes can you make by shading triangles or squares?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.