Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
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.
A Sudoku with a twist.
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Two sudokus in one. Challenge yourself to make the necessary
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
A Sudoku that uses transformations as supporting clues.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
How many models can you find which obey these rules?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?