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?
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 pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with a twist.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
A Sudoku with clues given as sums of entries.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku with clues as ratios.
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
A Sudoku that uses transformations as supporting clues.
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
How many models can you find which obey these rules?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
How many different symmetrical shapes can you make by shading triangles or squares?
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
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
This task follows on from Build it Up and takes the ideas into three dimensions!
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!