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

out of my mind quetion, Lolzzzzzz

you want pattern on the tile

or the pattern for the tile placement

or the pattern for the tile placement

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

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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[[][][][][][][][]]

[[][][][][][][][]]

[[][][][][][][][]]

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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!!

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

XPT: What's the answer you were expecting?

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
likes this

Nice question.

So you get the $

So you get the $