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2014-07-18, 18:33   #1
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

3×367 Posts
Rugged Challenge

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
Attached Files
 Matt puzzle.pdf (255.4 KB, 174 views)

 2014-07-18, 19:34 #2 rogue     "Mark" Apr 2003 Between here and the 19·347 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 3·367 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 2·5·137 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.
2014-07-20, 03:26   #5
axn

Jun 2003

23×233 Posts

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?

2014-07-20, 13:53   #6
lavalamp

Oct 2007
Manchester, UK

101010110102 Posts

I prettified my answer. For those who wish to see, re-save the attached file with the extension .html instead of .txt
Attached Files
 rugged.txt (6.1 KB, 166 views)

 2014-07-22, 03:37 #7 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 3·367 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 25328 Posts I'd be interested to see Rogue's solution where one piece is flipped.
2014-07-29, 16:09   #9
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

3·367 Posts

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

Regards,
Matt
Attached Files
 Matt puzzle answer 1.pdf (214.4 KB, 135 views)

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