Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Four small numbers give the clue to the contents of the four
Two sudokus in one. Challenge yourself to make the necessary
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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 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.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This Sudoku, based on differences. Using the one clue number can you find the solution?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A Sudoku that uses transformations as supporting clues.
This Sudoku combines all four arithmetic operations.
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.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
In how many ways can you stack these rods, following the rules?
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.
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
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A Sudoku with a twist.
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?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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.
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
A Sudoku with clues as ratios.
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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 find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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?