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.
Four small numbers give the clue to the contents of the four
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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. . . .
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Two sudokus in one. Challenge yourself to make the necessary
A Sudoku that uses transformations as supporting clues.
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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?
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?
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 combines all four arithmetic operations.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
A Sudoku with a twist.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
In how many ways can you stack these rods, following the rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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
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.
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.
Use the differences to find the solution to this Sudoku.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?