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?

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?

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

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

A pair of Sudoku puzzles that together lead to a complete solution.

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?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

You need to find the values of the stars before you can apply normal Sudoku rules.

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

A Sudoku that uses transformations as supporting clues.

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

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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.

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

Use the clues about the shaded areas to help solve this sudoku

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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?

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.

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting 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. . . .

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

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

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

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?

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

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

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

A Sudoku with clues given as sums of entries.

A Sudoku based on clues that give the differences between adjacent cells.

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.

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?

Solve the equations to identify the clue numbers in this Sudoku problem.

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

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.

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 been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?