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.
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
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?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
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?
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.
My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
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?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
A Sudoku with clues as ratios or fractions.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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!
A Sudoku with a twist.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
A Sudoku with clues as ratios.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Four small numbers give the clue to the contents of the four
Use the differences to find the solution to this Sudoku.
You need to find the values of the stars before you can apply normal Sudoku rules.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow