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?

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?

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?

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.

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

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

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

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 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.

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.

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?

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

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

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

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

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. . . .

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

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

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 that uses transformations as supporting clues.

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

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.

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

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

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.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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

A Sudoku with clues given as sums of entries.

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

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.

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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 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.

Use the differences to find the solution to this Sudoku.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Find out about Magic Squares in this article written for students. Why are they magic?!