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.

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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 your logic?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Two sudokus in one. Challenge yourself to make the necessary connections.

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?

Two sudokus in one. Challenge yourself to make the necessary connections.

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

A Sudoku that uses transformations as supporting clues.

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 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.

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite 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.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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.

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.

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.

Four small numbers give the clue to the contents of the four surrounding cells.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

This Sudoku, based on differences. Using the one clue number can you find the solution?

This Sudoku requires you to do some working backwards before working forwards.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Solve the equations to identify the clue numbers in this Sudoku 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?

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.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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?

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. . . .

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

How many models can you find which obey these rules?

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.

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?

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 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.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

How many different triangles can you make on a circular pegboard that has nine pegs?