In a week of pentominoes, there is a little game that uses tetrominoes – Tetris. Now, as we have seen, there are 12 free pentominoes. As each pentomino has an area of 5 unit squares, all 12 pentominoes have a combined area of 60 square units. The problem of tiling a rectangle of 60 square units with one each of the 12 pentominoes has numerous solutions.
In contrast, there are just 5 free tetrominoes, each obviously has an area of 4 square units. However, it is impossible to tile any rectangle of 20 square units using one each of all 5 tetrominoes.
Why is this impossible?
[Cartoon is from xkcd, who else!]
Feel free to comment, ask questions and even check your answer in the comments box below powered by
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.