Monday, May 7, 2012

No fault lines

Build a rectangle with multiple 2x1 bricks such that the rectangle has no "fault lines".  A fault line is a straight line through the rectangle that does not cut through any of the bricks.

For example, the following rectangle fails because of the fault line indicated in red.
What's the smallest rectangle you can make without fault lines?  You may send solutions to skepticsplay at gmail dot com.

Can you do the same with 3x1 bricks?

This puzzle is taken from Polyominoes: Puzzles, Patterns, Problems, and Packings, by Solomon W. Golomb.

See solutions
at

11 comments:

  1. AnonymousMay 7, 2012 at 11:14 AM

    a single 2x1 brick

    ReplyDelete
  2. millerMay 7, 2012 at 11:55 AM

    But you need to use multiple bricks.

    ReplyDelete
  3. AnonymousMay 7, 2012 at 1:50 PM

    Three.

    ReplyDelete
  4. millerMay 7, 2012 at 7:00 PM

    More than three are necessary. If you need to verify a solution you can send it to me.

    ReplyDelete
  5. blahsMay 8, 2012 at 6:07 AM

    I wanna say 5x4...

    ReplyDelete
  6. millerMay 8, 2012 at 8:07 AM

    It's not enough to guess the best size, you have to construct a solution! 5x4 is not possible.

    ReplyDelete
  7. Eduard BaumannMay 8, 2012 at 12:09 PM

    aabbc
    bccac
    bddab
    caccb
    cabaa
    ddbcc
    is a 5x6 case. Smallest?

    ReplyDelete
  8. millerMay 8, 2012 at 12:46 PM

    Yes, 5x6 is the smallest possible solution! I believe there are other unique forms though.

    ReplyDelete
  9. midoriMay 9, 2012 at 12:58 AM

    Oh hey, 5x6 is the smallest? I found a 5x6 solution.

    No, nevermind, now that I look closely it's just like Eduard Baumann's solution, only flipped.

    ReplyDelete
  10. D2000September 2, 2012 at 12:49 PM

    This comment has been removed by the author.

    ReplyDelete
  11. D2000September 2, 2012 at 12:51 PM

    A B C C D D
    A B E F F G
    H H E I J G
    K L L I J M
    K N O OM

    ReplyDelete

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