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

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?

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.

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?

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

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.

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

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

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 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?

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

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.

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

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.

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

A Sudoku that uses transformations as supporting clues.

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.

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

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.

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

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

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

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

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

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.

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

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

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

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

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 requires you to do some working backwards before working forwards.

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.

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?

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?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

A challenging activity focusing on finding all possible ways of stacking rods.

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.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

How many different symmetrical shapes can you make by shading triangles or squares?