Rugged Challenge

MattcAnderson · 2014-07-18, 18:33

Hi Fun Math People,

I have a fun puzzle.

A rug has a hole in it as shown.

Is it possible to create a square rug by cutting the existing rug into exactly two pieces?

In case you can't see the attachment, the rug measures 12 feet by 9 feet with a one foot by 8 foot hole in its center.

Regards,
Matt

rogue · 2014-07-18, 19:34

If you can flip sections of the rug upside down, then yes, but maybe someone has a solution that doesn't require that.

MattcAnderson · 2014-07-19, 00:15

At least the square footages come out right.
12*9 = 108
minus the 8 square foot hole gives
100 square feet for the 10 by 10 sown up rug.

I will wait a few days and then post the answer.

Regards,
Matt

lavalamp · 2014-07-19, 23:49

I have a solution that does not require flipping one of the pieces over.

Not sure how to post it without it being a spoiler though. Plus the margins are too small, etc. etc.

axn · 2014-07-20, 03:26

Quote:

Originally Posted by lavalamp

Not sure how to post it without it being a spoiler though. Plus the margins are too small, etc. etc.

Posting as an attachment is automatically spoilerised, innit?

lavalamp · 2014-07-20, 13:53

I prettified my answer. For those who wish to see, re-save the attached file with the extension .html instead of .txt

MattcAnderson · 2014-07-22, 03:37

LavaLamp has the right answer. Cut one foot over and two feet down and make stair steps like that to the bottom of the hole, and then another set of steps from the top of the hole to the side.

Regards,
Matt

lavalamp · 2014-07-22, 10:13

I'd be interested to see Rogue's solution where one piece is flipped.

MattcAnderson · 2014-07-29, 16:09

Here is a .pdf document. Rugged Challenge is problem #12.

Regards,
Matt

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2014-07-18, 19:34	#2
rogue "Mark" Apr 2003 Between here and the 6347₁₀ Posts	If you can flip sections of the rug upside down, then yes, but maybe someone has a solution that doesn't require that.

2014-07-19, 00:15	#3
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 320₁₆ Posts	At least the square footages come out right. 12*9 = 108 minus the 8 square foot hole gives 100 square feet for the 10 by 10 sown up rug. I will wait a few days and then post the answer. Regards, Matt

2014-07-19, 23:49	#4
lavalamp Oct 2007 Manchester, UK 10101001011₂ Posts	I have a solution that does not require flipping one of the pieces over. Not sure how to post it without it being a spoiler though. Plus the margins are too small, etc. etc.

2014-07-22, 03:37	#7
MattcAnderson "Matthew Anderson" Dec 2010 Oregon, USA 1440₈ Posts	LavaLamp has the right answer. Cut one foot over and two feet down and make stair steps like that to the bottom of the hole, and then another set of steps from the top of the hole to the side. Regards, Matt

2014-07-22, 10:13	#8
lavalamp Oct 2007 Manchester, UK 2513₈ Posts	I'd be interested to see Rogue's solution where one piece is flipped.