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Tiling puzzle

Discussion in '$1 Daily Competition' started by xpi0t0s, Sep 24, 2009.

  1. xpi0t0s

    xpi0t0s Mentor

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    I'm tiling my kitchen floor and have a pack of 82 identical square tiles. I'd like to use all of them, and to arrange them into a large square. I don't mind cutting some of the tiles exactly in half. The grouting may vary slightly but must appear even to a casual observer. Can you suggest a pattern?
     
  2. sameer_havakajoka

    sameer_havakajoka New Member

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    out of my mind quetion, Lolzzzzzz
     
  3. nimesh

    nimesh New Member

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    you want pattern on the tile
    or the pattern for the tile placement
     
  4. xpi0t0s

    xpi0t0s Mentor

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    It'd be nice to see some attempts before I post the solution.
     
  5. Mridula

    Mridula New Member

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    Is it
    1. 8x8 = 64 tiles use to make a proper square
    2. Then, 16 out of 18 tiles, will be used to patch the 4 border by cutting each one of them half
    3. Then left out 2 tile2, use it glue the extra 4 corners of the square
     
  6. Mridula

    Mridula New Member

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    [ - - - - - - - - ]
    [[][][][][][][][]]
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    [[][][][][][][][]]
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    [ - - - - - - - - ]

    8x8 = 64 tiles
    18 tiles are left, cut each them completely half
    Then use 10 half tiles, on sides like 5 at each sides
    8 tiles are left
    Then cover the top and bottom with 4 (cut in to half) on top and bottom

    In the picture, I could not put properly the last and top line!!
     
  7. nimesh

    nimesh New Member

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    Using 8*8 and then using 0.5 tiles around each sides, we would be able to achieve
    as described in the attached image (1) , which is similar to Mridula's reply... :)

    tiling.jpg

    till this step we would be able to use 80 tiles, but it would not come to a perfect square

    If the tiles are identical from all the 4 corners also, then if we move the any of the 2 opposide sides comprising of all 0.5 tiles we would be able to fit 1 more tile (0.5 on top and 0.5 at bottom) as in the attached image (2)

    tiling1.jpg

    We would still have 1 tile left :(
     
  8. nimesh

    nimesh New Member

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    XPT: What's the answer you were expecting?
     
  9. xpi0t0s

    xpi0t0s Mentor

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    OK then. This is the floor pattern at a church I used to attend. The outer square is 9x9, but I counted 50 tiles (40 complete and 10 split diagonally) in the middle for a total of 82 tiles. I thought it was an interesting layout and it occurred to me a few days ago it might make a good puzzle.
     

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  10. nimesh

    nimesh New Member

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    Nice question. :)

    So you get the $ :2thumbsup
     
  11. shabbir

    shabbir Administrator Staff Member

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    Congrats XP and effective use of observing things around.
     
  12. SaswatPadhi

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

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    Nice question and observation xpi0t0s :)

    5 * sqrt(2) = 7.0710 = 7 (approx.)
    Nice.
     

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