Polyominoes
and Recreational Mathematics
Written and compiled by Dan Klarskov
What are
polyominoes?—Think of polyominoes as small clusters
of giantsized 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 multiplesquare 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 bestknown
polyominoes are the 12 pentominoes. The first pentominorelated
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
80page 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
