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?

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 activity investigates how you might make squares and pentominoes from Polydron.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

A Sudoku that uses transformations as supporting clues.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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.

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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

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