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?

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

[ - - - - - - - - ] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [[][][][][][][][]] [ - - - - - - - - ] 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!!

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... 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) We would still have 1 tile left

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.