8 Jul 2013

Pentomino Games and Puzzles: Upper Primary Mathematics

A pentomino is a flat figure made from five unit squares joined along an edge. In the diagram below, figures P and Q are pentominoes but figure R is not.

If you think of each pentomino as a flat shape that can be moved around the plane, then P and Q are two distinct pentominoes. There is no way that we can rotate the P shape so that it matches the Q shape.

How many distinct flat pentominoes can you find?

If you now think of each pentomino as a physical tile that you can hold in your hand, you can easily see that figures P and Q are reflections of each other – you can flip one over and it looks like the other one. These are known as ‘free’ pentominoes.

How many distinct free pentominoes can you make? (As P and Q now count as just one shape, there are fewer free pentominoes than flat ones!)

Warm-up over, let’s get down to the real question! If you are only allowed P and Q pentominoes, in how many ways can you tile the following rectangles, making sure there are no gaps, no overlaps and no overhangs?

a)  5x4 . . . . . . . . . . b)  5x8 . . . . . . . . . . c)  5x10 . . . . . . . . . .

I can hear you thinking:”That’s nice, but where’s the game?!” Here it is: Pentamino (for Windows). Simple to install and... simply frustrating!

If you prefer an online game - and an easier starting level - then try the Pentominoes Game at Scholastic.

Pentominoes also makes an interesting 2 or 3 player game. Taking turns, the aim is to create ‘holes’ in the grid that no pentomino pieces can fit into. However, your opponent is trying to do the same thing. The winner is the last player who has successfully placed a piece on the board.

There are numerous implementations of pentominoes as both a game and a puzzle. If you find one you particularly like, let everyone know in a comment below.

Feel free to comment, ask questions and even check your answer in the comments box below powered by Disqus Google+.

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.

No comments:

Post a Comment

Related Posts Plugin for WordPress, Blogger...