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Games take Shape

This site is in two parts:

Games With Pentominoes

Just as the shape of a domino is made up of two squares, shapes made from five squares are called pentominoes.

The simplest pentomino is:

pentomino

There are other pentominoes, for example:

pentomino

Pentominoes are most fun if they can be picked up and moved around. Moving around includes turning over, so we make the rule that both of these count as the same shape:

pentomino  

and

  pentomino

Similarly, though these three look different they are actually all the same shape:

pentomino

The first challenge is for you to discover all the possible pentominoes.
Remember: squares must be connected by whole sides, not by part sides or corners, and two shapes are considered identical if they can be moved or turned so they are the same.

Try this first before you look at the answers below!

How many can you find?

There are actually twelve pentominoes to be found:

pentomino

Something to think about?

  • Since all the pentominoes are made up of five squares they all have the same area, but do they have equal perimeters?
  • Explain why a full set of pentominoes occupies 60 squares.

Another Challenge...

  • Can you fit all twelve, jigsaw-like, into a 12 x 5 rectangle. Be warned that, though there are many solutions, this is not at all easy.
  • If that is too difficult, try fitting just six pentominoes into a 6 x 5 rectangle.
    This is one solution:

pentomino

Game: Pentomino Chess

A set of pentominoes whose squares are the same size as a those on a chessboard offer an excellent game which is simple enough to be learned by Key Stage 1 pupils and demanding enough to challenge A level students.

The rules could hardly be easier.
Two players take turns to choose a pentomino and place it on a squared board. All pieces must be placed so they cover five whole squares on the board - pieces may not be placed at an angle, or covering part squares. If you find yourself unable to place a piece you lose the game.

It's a good idea to begin on a 5x5 board, even though whoever plays first has an easy win! Can you work out how?

DON'T LOOK YET!

Here's how to do it...

  • The first player places the long pentomino down the centre column.

  • The second player plays into either the left or the right blank area and the first player then plays into the other. No further pieces can be placed, so the second player loses.

You can make up your own rules:

  • forbid the first player from making this move. The game now becomes much less obvious.

  • players could move up to a 6x6 board. (The 8 by 8 board is very difficult!)

Other 'Maths Takes Shape' games to try out:

CONTINUO - a pocket money game laying tiles to form coloured paths. Other versions (e.g. TRIANGULO CONTINUO) are also available.

A family game suitable for all ages, from Reception to adult.

TRICKY - another pocket money game, and simple enough to learn in 30 seconds. Players pick up scoring counters from a pentagonal grid. It's a game of skill rather than luck, but that doesn't stop me regularly losing to Key Stage 1 children. The presentation is splendidly original - Tricky comes in a bag that is also two different boards.

Suitable for all Key Stages.

Tricky is produced by a local inventor: contact Mr Chris Cowsley, 64 Tannery Drift, Royston, SG8 5DE (phone 01763-241754).

The L-GAME was invented by Edward de Bono with the aim of being the simplest possible challenging strategic game.

  • It is played on a 4x4 square grid.
  • Each player owns one of the two L-pieces, and there are two further neutral pieces. The starting position is shown in the diagram.
  • When it is your turn to move you must move your own L to a new position; it may be rotated and/or turned over.
  • As long as at least one new square is covered the move is legal.
  • You may also - if you wish - move either of the two neutral N pieces to a new position. You win if you block your opponent's L so it cannot be moved.

L-GAME
Suitable for all Key Stages, particularly KS2 and above.

MULTIPUZZLE (Spear's Games) is a pocket money puzzle which has been available for many years. Multipuzzle is a collection of hexomino puzzles.

Suitable for KS2 and above.

GO-MOKU Two players, Black and White, take turns to place counters on a square grid. The first to make a line (horizontal, vertical, or diagonal) of five wins. Go-Moku is a traditional game for Japanese children who play on an 18x18 board, but beginners can use an ordinary chessboard.

Most suitable for KS2 and upwards.

CONNECT-4 is a well-known simple version of Go-Moku.

It is suitable for all Key Stages.

HIP is similar to Go-Moku, but the aim is to place four counters not in a line, but at the corners of a square. The sides of the square do not have to be parallel to the edges of the board, and other counters may lie between those making the square, so the game provides excellent practice in recognising squares of different orientations and sizes.

Suitable for upper KS2 and above.

THE POISONED CHOCOLATE BAR One square of a bar of chocolate is poisoned. Players take turns to shade in squares on the bar of chocolate; in your turn you may shade in any number of squares, but you must shade in a complete rectangle (e.g. 3x2, 4x1, 2x2, 1x1). The player who shades in the poisoned square loses the game.

The board may be of any size and the poisoned square may be in any position. The game not only requires strategic thinking, but also is as good a way as any of reminding children that the set of rectangles includes squares as well as oblongs.

Suitable for all Key Stages.

SIM is a pencil and paper game. Six points are marked out in a hexagon. The first player chooses any two of the points and joins them with a red line. The second player joins any two points with a blue line. Players continue until one player forms a triangle of their own colour; this player loses.

In this game, Blue (dotted lines) has lost by completing the triangle CDF.

Suitable for all Key Stages

GO is one of the world's great strategy games. The rules are much simpler than chess, but Go is at least as deep. Players place counters on a square grid with the aim of surrounding territory. Go is the classic game of Japan; it originated as Wei-ch'i in China more than 3000 years ago.

The British Go Association produces materials for schools and offers speakers to introduce the game to pupils. Contact Simon Goss (01344-777963) for information.

TILING GENERATORS and MATs (Mathematical Activity Tiles) are rich resources for designing puzzles and games and for performing other investigations. They are made from similar material to beermats; 3-D as well as 2-dimensional shapes can be made. Details may be obtained from the Association of Teachers of Mathematics, 7 Shaftesbury Street, Derby, DE23 8YB (phone 01332-346599; fax 01332-204357)

Suitable for all Key Stages.

Do please feel free to contact me with enquiries about these or other games:

Alan Parr
6 Longfield Gardens
Tring
HP23 4DN

Tel: 01442-824173
Fax: 070-920-24173
Email: df08@dial.pipex.com