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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?
A Sudoku with a twist.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues given as sums of entries.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Two sudokus in one. Challenge yourself to make the necessary connections.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A Sudoku with clues as ratios.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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?
A Sudoku that uses transformations as supporting clues.
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?
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.
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
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. . . .
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?
Four small numbers give the clue to the contents of the four surrounding cells.
How many different symmetrical shapes can you make by shading triangles or squares?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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?
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.
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 of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
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?
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
How many models can you find which obey these rules?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A few extra challenges set by some young NRICH members.