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Tiling puzzle

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

  1. xpi0t0s

    xpi0t0s Mentor

    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

    out of my mind quetion, Lolzzzzzz
     
  3. nimesh

    nimesh New Member

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

    xpi0t0s Mentor

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

    Mridula New Member

    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

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

    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

    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

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

    xpi0t0s Mentor

    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.
     

    Attached Files:

  10. nimesh

    nimesh New Member

    Nice question. :)

    So you get the $ :2thumbsup
     
  11. shabbir

    shabbir Administrator Staff Member

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

    SaswatPadhi ~ Б0ЯИ Τ0 С0δЭ ~

    Nice question and observation xpi0t0s :)

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

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