We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you coach your rowing eight to win?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
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.
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?
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?
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 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.
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. . . .
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?
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the products of adjacent cells, can you complete this Sudoku?
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku with clues as ratios.
A Sudoku with a twist.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A pair of Sudoku puzzles that together lead to a complete solution.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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.
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. . . .
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Two sudokus in one. Challenge yourself to make the necessary
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.
This Sudoku combines all four arithmetic operations.
This challenge extends the Plants investigation so now four or more children are involved.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
How many different symmetrical shapes can you make by shading triangles or squares?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?