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?

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?

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?

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?

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

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.

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

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.

A Sudoku that uses transformations as supporting clues.

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

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.

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

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?

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

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.

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.

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

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.

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.

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

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.

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

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

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.

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?

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.

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

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.

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

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 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?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.