Klarskov Puzzles
Udfordrende kvalitets puslespil i træ

Polyominoes and Recreational Mathematics
Written and compiled by Dan Klarskov

What are polyominoes?—Think of polyominoes as small clusters of giant-sized pixels.

In 1953, Solomon W. Golomb ”invented” the name polyominoes in a speach to the Harvard Mathematics Club. A year after its delivery, Golomb`s Harvard talk was published in American Mathematical Monthly, where it attracted the attention of a number of professional mathematicians. However, it was the reprinting by Martin Gardner of some of this material in the May 1957 issue of Scientific American that brought polyominoes to the attention of a vast reading public.

Golomb derived the names for multiple-square combinations ("polyominoes") from the word "dominoes", which are two squares joined. All the possible shapes formed from the same number of congruent squares have their specific ranking name: the 2 trominoes have 3 squares; the 5 tetrominoes have 4 (that's the ones in the popular Tetris computer game); the 12 pentominoes have 5; the 35 hexominoes have 6; the 108 heptominoes have 7; the 369 octominoes have 8 squares each, etc.

The best-known polyominoes are the 12 pentominoes. The first pentomino-related problem, though not by that name, was published in 1907 in The Canterbury Puzzles, written by the great English inventor of puzzles, Henry Ernest Dudeney. Moreover, an extensive literature on the subject (under the heading of “dissection problems”) had appeared during the 1930s and 1940s in the Fairy Chess Review, a British puzzle journal.

Quintillions
Kate Jones’s Kadon Enterprises was started up in 1979 and incorporated in 1980. One of its flagship products is Quintillions, a nice set of wooden pentominoes with a great 80-page booklet, with a lot of nice tasks to solve. One of these tasks is a “progression” that lets the puzzler create a 5x3 rectangle, then 5x4, 5x5, 5x6, 5x7 and all the way up to the 5x12 rectangle. More information about Kadon Enterprises inc. here.

The Katamino
“The Katamino puzzleboard was discovered after Andre Perriolat brought his son a set of wooden pentominoes for Christmas and a wooden rectangle to fit them into. After a few hours of studious dedication, the son managed to put the pentominoes into the rectangle and resumed watching TV. In order to get better value for the money, Mr. Perriolat challenged his son to make a 5x4 rectangle. Having completed this, Mr. Perriolat then challenged his son to make a 5x5 rectangle, then a 5x6, then 5x7 and so on. Katamino was born.”

What Perriolat did with Kate Jones’s 1979 Quintillions/pentomino progression task was to use a box with a divider. The box is a 5x13 rectangle. This box includes the 5x12 task plus space for a divider. More about the great Katamino game here.

To me the Katamino game is a Pentomino Step Game with a divider. It uses the 12 pentominoes on a puzzleboard to solve the 9 rectangle progressions, and the divider changes the playing area, step by step.

We are happy to answer any questions, contact Dan at:
dan@klarskov.net

Hvis du har et spørgsmål er du velkommen til at skrive til Dan her:
dan@klarskov.net


More:

Quintillions


The Katamino