Special Issue: January 3, 2002

Mathematics Fun

Polyominoes

A polyomino is a geometric figure that is formed by squares that share at least one whole side.

Monomino
Domino
Tromino

The names for polyominoes tell the number of squares from which each type is formed:

• Mono- means "one", so a monomino has 1 square
• Di- means "two," so a domino has 2 squares
• Tri- means "three," so a tromino has 3 squares
• Tetra- means "four", so a tetromino has 4 squares
• Penta- means "five," so a pentomino has 5 squares
• Hexa- means "six," so a hexomino has 6 squares
• Hepta- means "seven," so a heptomino has 7 squares
• Octo- means "eight," so an octomino has 8 squares

Do you know what language these number prefixes come from?
Answer

Tetrominos

You may have seen tetrominos if you've ever played the game Tetris. There are five possible configurations of tetrominos.

One handy way to remember the five tetromino shapes is the mnemonic phrase "square lint." One of the five shapes is a square; the remaining shapes resemble the letters 'L', 'I', 'N', and 'T'.

Puzzlers

1. How many tetrominoes are needed to tile an area that is 4 units by 8 units? (Use graph paper for the grid, or print the 4 by 8 grid provided. Create the 5 tetromino shapes using graph paper, or print the patterns page and cut out each shape.) Try this with each tetromino shape. Can you completely cover the area using each shape by itself?
   Solutions
   
   
2. How many different ways can pentominoes (polyominoes made with 5 squares) be formed? How about hexominoes, heptominoes, and octominoes?
   Answer
   
   

3. If cubes are used instead of squares, the resulting three-dimensional shapes are called polycubes. There are 8 tetracubes and 29 pentacubes. Can you figure out why there are more tetracubes than tetrominoes, and more pentacubes than pentominoes?

Bonus Question

How many words can you think of using the pentominoes letters (F', 'L', 'I', 'P', 'N', 'T', 'U', 'V', 'W', 'X', 'Y', and 'Z').?

Just For Fun: Connect-The-Dots

What shape do you see when you connect the dots?