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Old 08-05-2010, 06:35 PM   #1
pdurrant
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Carpet Cutting Puzzle

Time for another puzzle. I found this one at a puzzle site in the Netherlands. Despite having a Dutch web address, the site appears to be entirely in English.

Anyway, here's the puzzle:

I have a room that's 9 metres by 12 metres, and I'm going to have an 8 metre by one metre aquarium right in the middle of it (lengthways).

Quickly noticing that the area of open floor will be exactly 100 metres (9x12-8), I buy a 10 metre by 10 metre carpet that was going cheap on eBay. But how to cut it to fit the shape? I don't want to cut the carpet more than necessary. What's the smallest number of pieces I must cut the 10x10 metre carpet into, to make it fit the 12x9 space, with the 8x1 hole in the middle? Hint: It's less than four.

I've attached the picture of the situation take from the above web site.

Answers in
Spoiler:
spoiler tags
if possible, please.

I hope this non-verbal, non-numerical, non-logic puzzle will make a nice change.
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Last edited by pdurrant; 08-07-2010 at 04:11 PM. Reason: Removed unhelpful transparency from the picture. Added upper limit to number of pieces.
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Old 08-06-2010, 01:10 AM   #2
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I'll take a shot at it.
Spoiler:
Well, my answer is 4 pieces of carpet.
A 1x8 piece
A 1x9 piece
A 1x1 piece
and a 10x9 piece with a 1x8 cut out from it to align with the aquarium so it kind of looks like the letter C.
Hopefully this makes sense.
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Old 08-06-2010, 04:20 AM   #3
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Quote:
Originally Posted by noonionclub View Post
I'll take a shot at it.
Spoiler:
Well, my answer is 4 pieces of carpet.
A 1x8 piece
A 1x9 piece
A 1x1 piece
and a 10x9 piece with a 1x8 cut out from it to align with the aquarium so it kind of looks like the letter C.
Hopefully this makes sense.
A good try, but there is a solution using far fewer pieces.
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Old 08-06-2010, 05:41 AM   #4
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Old 08-06-2010, 09:32 AM   #5
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Quote:
Originally Posted by pdurrant View Post
Quickly noticing that the area of open floor will be exactly 100 metres (9x12-8), I buy a 10 metre by 10 metre carpet that was going cheap on eBay. But how to cut it to fit the shape? I don't want to cut the carpet more than necessary. What's the smallest number of pieces I must cut the 10x10 metre carpet into, to make it fit the 12x9 space, with the 8x1 hole in the middle?
I'm no interior designer, but this is just awful. Besides having a carpet that's all cut up, the room has no space for any furniture. Though since there is a huge aquarium in the middle, it'd be an onerous task moving anything in besides a card table and some folding chairs.

Anyway:
Spoiler:

The smallest I can figure it to be is three cuts (four pieces):
1) Cut two 4x10 pieces, and then cut off a 1x2 piece from the remaining 2x10.

331111111111
331111111111
331111111111
331111111111
33________44
332222222222
332222222222
332222222222
332222222222

or

2) Cut off a 1x10 strip, cut a 1x1 square from the end of that strip, and then cut out a 1x8 strip from the middle of the remaining 9x10 square.

143333333333
143333333333
143333333333
143333333333
14________33
143333333333
143333333333
143333333333
123333333333

I can't imagine doing it in 2 cuts, but I'll keep trying.
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Old 08-06-2010, 01:31 PM   #6
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Try this:

Spoiler:
Three cuts.
Take the carpet and cut out a 2 by 10 piece from the middle. You will now have two 10 by 4 pieces to put along the 12 meter walls. Next cut off a 1 by 2 piece off the strip. lay the 2 by 9 piece across the bare part of the room. Take the 1 by 2 piece to cover the middle spot on the other end. You will now have a 1 by 8 cutout in the center of a 12 by 9 carpet.
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Old 08-06-2010, 02:41 PM   #7
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Here's My Attempt

So excited. My first try at solving one of your puzzles (I usually have to give up and peek at the spoilers)!

Spoiler:
Take the 10 x 10 carpet and cut twice: Two pieces will be 10 x 4 and one will be 10 x 2.

Cut the 10 x 2 piece so that you've got a 9 x 2 and a 1 x 2 piece.

Then, you put them together so the two 10 x 8 pieces are horizontal with the 9 x 2 piece butting up against them vertically on one side. Use the little 1 x 2 piece on the other side to finish off the empty space.

This explanation comes out better if I could show a picture, but since I've just figured out how to use spoiler tags, I'll just say "pic available upon request."


How'd I do?

Marilyn

Last edited by Mickey330; 08-06-2010 at 02:42 PM. Reason: Durn grammar!
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Old 08-06-2010, 02:46 PM   #8
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Quote:
Originally Posted by GeoffC View Post
noonionclub

Welcome to mobileread ....
Thanks G. I've been a lurker for some time and decided to add my input to the wonderful puzzles that pdurrant has been providing.

Thanks pdurrant for providing me a use for my brain power besides reading all the time and watching movies. Lol. Keep up the good work.

Was trying to get fewer cuts and I still can't figure it out.
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Old 08-06-2010, 03:55 PM   #9
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Quote:
Originally Posted by clarknova View Post
I'm no interior designer, but this is just awful. Besides having a carpet that's all cut up, the room has no space for any furniture. Though since there is a huge aquarium in the middle, it'd be an onerous task moving anything in besides a card table and some folding chairs.

Anyway:
Spoiler:

The smallest I can figure it to be is three cuts (four pieces):
1) Cut two 4x10 pieces, and then cut off a 1x2 piece from the remaining 2x10.

331111111111
331111111111
331111111111
331111111111
33________44
332222222222
332222222222
332222222222
332222222222

or

2) Cut off a 1x10 strip, cut a 1x1 square from the end of that strip, and then cut out a 1x8 strip from the middle of the remaining 9x10 square.

143333333333
143333333333
143333333333
143333333333
14________33
143333333333
143333333333
143333333333
123333333333

I can't imagine doing it in 2 cuts, but I'll keep trying.
Good tries, but it's possible to do it with fewer pieces.
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Old 08-06-2010, 03:55 PM   #10
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Quote:
Originally Posted by obs20 View Post
Spoiler:
Three cuts.
Take the carpet and cut out a 2 by 10 piece from the middle. You will now have two 10 by 4 pieces to put along the 12 meter walls. Next cut off a 1 by 2 piece off the strip. lay the 2 by 9 piece across the bare part of the room. Take the 1 by 2 piece to cover the middle spot on the other end. You will now have a 1 by 8 cutout in the center of a 12 by 9 carpet.
Good try, but it's possible to do it with fewer pieces.
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Old 08-06-2010, 03:57 PM   #11
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Quote:
Originally Posted by Mickey330 View Post
So excited. My first try at solving one of your puzzles (I usually have to give up and peek at the spoilers)!

Spoiler:
Take the 10 x 10 carpet and cut twice: Two pieces will be 10 x 4 and one will be 10 x 2.

Cut the 10 x 2 piece so that you've got a 9 x 2 and a 1 x 2 piece.

Then, you put them together so the two 10 x 8 pieces are horizontal with the 9 x 2 piece butting up against them vertically on one side. Use the little 1 x 2 piece on the other side to finish off the empty space.

This explanation comes out better if I could show a picture, but since I've just figured out how to use spoiler tags, I'll just say "pic available upon request."


How'd I do?

Marilyn
As with the other solutions proposed so far, I think yours works, but it's possible to do it in fewer pieces.
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Old 08-06-2010, 03:58 PM   #12
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What's the smallest number of pieces I must cut the 10x10 metre carpet into, to make it fit the 12x9 space, with the 8x1 hole in the middle?
Perhaps I should say that the answer is less than four pieces.
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Old 08-07-2010, 07:26 AM   #13
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Hopefully !

Spoiler:

Cut a 1 * 10 slice from one edge of the carpet and from one end of this slice remove 1 * 1 >> 2 pieces [ 1 * 9 & 1 * 1 ]

Cut a 1 * 8 piece into the middle of the remaining 10 * 9, from one of the shorter edges >> 1 large "U" shaped piece.

Lay the 1 * 8 piece to close off the "U" and add the 1 * 1.
Lay the 1 * 9 to complete.

3 pieces cut....

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Old 08-07-2010, 01:12 PM   #14
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Quote:
Originally Posted by GeoffC View Post
Hopefully !

Spoiler:

Cut a 1 * 10 slice from one edge of the carpet and from one end of this slice remove 1 * 1 >> 2 pieces [ 1 * 9 & 1 * 1 ]

Cut a 1 * 8 piece into the middle of the remaining 10 * 9, from one of the shorter edges >> 1 large "U" shaped piece.

Lay the 1 * 8 piece to close off the "U" and add the 1 * 1.
Lay the 1 * 9 to complete.

3 pieces cut....

Your solution works, but it's possible to do better than the four pieces of carpet you ended up with.
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Old 08-07-2010, 03:48 PM   #15
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I must say, there are much more ways to cut a carpet to 4 pieces than I suspected!
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