Tiling puzzle

xpi0t0s's Avatar, Join Date: Aug 2004
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?
0
sameer_havakajoka's Avatar
Skilled contributor
out of my mind quetion, Lolzzzzzz
0
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
you want pattern on the tile
or the pattern for the tile placement
0
xpi0t0s's Avatar, Join Date: Aug 2004
Mentor
It'd be nice to see some attempts before I post the solution.
0
Mridula's Avatar, Join Date: Mar 2008
Pro contributor
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
0
Mridula's Avatar, Join Date: Mar 2008
Pro contributor
[ - - - - - - - - ]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[[][][][][][][][]]
[ - - - - - - - - ]

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!!
0
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
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
0
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
XPT: What's the answer you were expecting?
0
xpi0t0s's Avatar, Join Date: Aug 2004
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 Images
File Type: jpg Greyfriars floor.jpg (29.4 KB, 7 views)
nimesh, SaswatPadhi likes this
0
nimesh's Avatar, Join Date: Apr 2009
Invasive contributor
Nice question.

So you get the $