Did you encounter any puzzle last week? Feel free to share it with us. Here is one that we stumbled upon figuring out the amount of tiles to buy to replace the old wood floor at the door entry. The area we want to cover is approximately 90" X 150". We want to use a pattern combining tiles of size 12" x 12" and 6" x 6". One large one and two small on top, creating together a rectangle of 12" x 18". Large tiles are sold in boxes, each holding tiles to cover 10 square foot. Smaller tiles are sold in boxes that each holds tiles to cover 6 square foot. How many boxes of each should we buy?

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## 4 comments:

Asumming it is 90 wide and 150 high/deep you will need 7.5 sets of tile to go the width and 8.3 sets to go the height. So you need 6 boxes of the 12" tiles (7.5 * 8 = 60, 10 per box) and 6 boxes of the 6" tiles (15 * 9 = 135, 24 per box). You will have 9 small tiles left over. You will have to cut 4 of the large tiles to complete the pattern on the end.

I would buy 6 boxes of big tiles and 5 boxes of small tiles.

I'll just rough it, because I think you will have some tiles left. It may also depend on direction, which is not specified, and which probably matters. And we didn't allow for any grout space so I'll leave that out. Each of your patterns is 18x12 (and 216 sqin) 13500squin/216 = 62.5 patterns.

Each pattern calls for one large tile and 2 small. You'll want 62 large tiles (6 boxes) and I think I'd choose to have small tiles at both "ends." Get 7 boxes (70) of large tiles, because you'll break some and may need some spares someday. For the smaller tiles, get maybe 70 patterns worth, spares for the same reason, 4 boxes. And some tile stores will let you return unopened boxes!! Tom

Here is the graphical demonstration of the answers

Both, Katrina and Tom, are right. Thank you so much for your insights.

Depending on the repetition of the pattern across the columns we may need different amounts of tiles and even boxes. Better have more than less.

I am glad I have the drawing now, to show to the contractor.

Katrina and Tom deserve a puzzle point each.

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