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#237 - Pentominoes (silver Tetris)

Forum Index -> Season 2 -> #237 - Pentominoes (silver Tetris) RSS

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#12383
#237 - Pentominoes (silver Tetris) 20/11/2008 16:24:47

arkasha
Lover of Puzzles

Messages: 125

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#237 Pentominoes

Front
A pentomino is a geometric chape formed by adjoining five squares with one another
edge to edge. There are twelve unique ways to do this, not counting rotations and
reflections:

Code:

     #
     # #   #                         #
  ## # #  ## ## ###     #   #    #  ## ##
 ##  # #  #  ##  #  # # #   ##  ###  #  #
  #  # ## #  #   #  ### ###  ##  #   #  ##
 
  F  I L  N  P   T   U   V   W   X   Y  Z


Classic pentomino problems involve trying to properly fill certain shapes with the twelve
pieces. For example, there are 1010 ways that one can arrange the pentominoes into a
5x12 rectangle. Here is one such example:

############
############
############
############
############

This figure is represented using the letter notations as follows:

Code:

 VVVWWFFNNNUU
 VTWWFFPPPNNU
 VTWZZFXPPYUU
 TTTLZXXXYYYY
 LLLLZZXIIIII


Note that the long "I-pentomino" is along the edge in the lower right corner.
How can you fill the same 5x12 rectangular area so that the I-pentomino is properly
contained in the interior of the configuration (i.e. no part of the I-pentomino touches
the edge of the 5x12 area)?

GUEST PUZZLE ARCHITECT
{ Eric Harshbarger }
Back
text to come


Please use this thread for discussion about this card.
My S2W2 solves: 49/86
#12555
Re: #237 - Pentominoes (silver Tetris) 28/11/2008 18:00:09

sloth007
Lover of Puzzles

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It may be the easiest Silver, but hey, I got a silver!

Spoiler: (highlight to read)

Now to pin down that taxing raccoon's vexing construct.

lol.
"Out on a limb!"
#13561
#237 - Pentominoes (silver Tetris) 03/04/2009 18:42:37

bionicben2
Lover of Puzzles

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Messages: 18

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it's really difficult, i have a set of wooden blocks from a puzzle that happened to be pentominoes, and even with a physical version it's excruciatingly difficult...
curse my ability!
#13563
#237 - Pentominoes (silver Tetris) 03/04/2009 20:42:26

fretty
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There is a nice trick to this one

Spoiler: (highlight to read)

just think about where else the straight piece could go if it isnt on the outside, then abuse the symmetry of the problem, to largely narrow down the number of possibilities.
My S2W2 solves - http://s2w2.perplexcitycardmanager.co.uk/cards/solved/fretty/

[image]
#13967
Re: #237 - Pentominoes (silver Tetris) 24/07/2009 17:09:16

volvox
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That's what I did, but I was nerd and wrote a Java program to iterate through the possibilities. You can also be smart about which ones you start with in order to fit around the "I". Still took quite a while to find the solution, however. Guess that's why some mathematician came up with a better algorithm for solving these types of problems.

Oh the things you end up learning from solving these cards!

Spoiler: (highlight to read)

In my research it looks like there are 1010 total solutions for the 5x12 rectangle, but I have a feeling only 4 or those (symmetry included) have the I pentomino not on the edge based on the results I've seen.
Abzot, my MoshiMonster
#13972
#237 - Pentominoes (silver Tetris) 24/07/2009 17:47:39

fretty
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I should imagine you have considered this but as a general hint to everyone:

Spoiler: (highlight to read)

There are only really a handful of possibilities for placing the I pentomino. Also consider rotations/reflections being the same, then after this you should be able to pinpoint the I pentomino to only a few places and work round it
My S2W2 solves - http://s2w2.perplexcitycardmanager.co.uk/cards/solved/fretty/

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