Renea Mielec

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PENTOMINOES

• Renea Mielec
• MA 341
• December 2, 1999

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Pentominoes

• Pentominoes are shapes that use five square
  blocks stuck together so that each square shares
  at least one whole side with another square.
• Classified as a polyomino - a category which also
  includes monominoes
• dominoes
• triominoes
• tetrominoes

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Basics of Pentominoes

• There are 12 different ways to organize
  pentominoes.
• They are often referred to by the letters they
  resemble.
• There are also pentacubes which are
  three-dimensional shapes formed from 5 cubes that
  touch each other on at least one side.

Graphic from http//lonestar.texas.net/jenicek/p
entomin/pentomin.html
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Pentomino History

• Polynominoes were brought to life by Solomon W.
  Golomb, 22 year old graduate student from Harvard
  University.
• He presented the topic at a Harvard Mathematics
  Club meeting in 1953. In his talk, he emphasized
  the general shapes formed from N unit squares.
• Although Golomb came up with the name, the idea
  of pentominoes has been around since 1907. Henry
  Ernest Dudeney published the first pentomino
  problem in his book, Canterbury Puzzles.

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Pentomino History cont.

• No major pentomino movement followed until Martin
  Gardner wrote about them in the journal
  Scientific American in 1957.
• People played with many different polyominoes but
  found the triominoes and tetrominoes to be
  slightly boring while the hexaminoes and
  heptominoes were too diverse. Yet, the 12
  pentominoes seemed to be just right.
• Later, Golomb wrote Polyonimoes in 1965.

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Pentomino Puzzles

• If you choose one of the pentominoes, you can
  construct a scaled duplicate of that specific
  pentomino using exactly nine of the remaining
  pentominoes.

• Numerous puzzles ask for a rectangle with sides
  3x20, 5x12, 4x15, or 6x10.
• There are 2339 solutions for a 6x10 rectangle,
  1010 solutions for a 5x12 rectangle, 368
  solutions for a 4x15 rectangle, and 2 solutions
  for a 3x20 rectangle.

Uses I, L, N, P, T, W, Z, V, Y
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Interesting Facts

• In the film 2001, A Space Odyssey, Arthur C.
  Clarke had the HAL Computer play pentomino games
  against astronaut Bowman.

Picture from http//uk.imdb.com/Title/title-exact
?0062622

• Pentominoes can be arranged
• in an Escherian fashion. For
• example, the W turns into F
• and X.

Graphic from http//pubweb.acns.nwu.edu/gbuehler
/speech.htm
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Guenter Albrecht-Buehler

• Dr. Albrecht-Buehler is the Robert Laughlin Rea
  Professor of Cell Biology at the Northwestern
  University Medical School in Chicago.
• In his spare time, he likes to create pictures
  using pentominoes.

Picture from http//pubweb.nwu.edu/gbuehler/gab.
htm
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At the Rio Grande, 48x32, 3/94
Battle With the Dragon, 32x48, 1/88
http//pubweb.nwu.edu/gbuehler/p117.htm
http//pubweb.nwu.edu/gbuehler/p44.htm
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• The Child, 32x48, 12/98

Rising Storm, 48x32, 11/98
http//pubweb.nwu.edu/gbuehler/pap4.htm
http//pubweb.nwu.edu/gbuehler/pap7.htm
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References

• http//pubweb.acns.nwu.edu/gbuehler/
• (various pages in the website)
• http//lonestar.texas.net/jenicek/pentomin/pentom
  in.html
• http//forum.swarthmore.edu/tour/pentominoes.html
• Martin, George E. Polyominoes A Guide to Puzzles
  and Problems in Tiling. The Mathematical
  Association of America, 1991.