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?
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?
Two sudokus in one. Challenge yourself to make the necessary
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?
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?
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 pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
A Sudoku with clues given as sums of entries.
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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.
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.
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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 NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
How many models can you find which obey these rules?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many different symmetrical shapes can you make by shading triangles or squares?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A Sudoku that uses transformations as supporting clues.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
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?