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?

# Tiling puzzle

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out of my mind quetion, Lolzzzzzz

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you want pattern on the tile

or the pattern for the tile placement

or the pattern for the tile placement

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

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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

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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!!

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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

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XPT: What's the answer you were expecting?

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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.

nimesh, SaswatPadhi
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Nice question.

So you get the $

So you get the $