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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Purple Puzzle Cards
#173-purple-circle set-the 14-15 puzzle
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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chichiri
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Joined: 31 Oct 2005
Posts: 207

 		#173-purple-circle set-the 14-15 puzzle
Sam Loyd (1841-1911) was born in philadelphia and lived in new york.
Loyd was one of the greatest puzzle designers of his time and the 14-15 puzzle was perhaps his most infamous. This puzzle was a traditional sliding tile puzzle, arranged just like the one below. The challenge was to move the 14 and 15 tiles back to their correct position.

Loyd offered a $1000 prize for the first correct solution, an enormous amount of money back then, but it was never claimed despite the thousands who say they performed the feat. He recounts that people became infatuated with the puzzle and ludicrous tales are told of shopkeepers who neglected to open their stores; of a distinguished clergyman who stood under a street lamp all through a wintry night trying to recall the way he had performed the feat. The mysterious feature of the puzzle is that none seem to be able to remember the sequence of moves whereby they feel sure they succeeded in solving the puzzle.

Instead of tormenting you with his original 14-15 puzzle, here is a slightly easier version. What is the shortest way to move the tiles in order to get the vacant square from the bottom right to the top left corner and to swap the 14 and 15 tiles?

see card catalog

that was a long one, succeeded is one of those words that just doesn't feel correct when you write it, well anyway thats all of my cards posted.

no da

PostPosted: Fri Nov 25, 2005 10:23 am
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Langley Moor
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Joined: 27 Oct 2005
Posts: 86

 		How many attempts have people managed to do this in? I've done it in 68, but that's wrong.... therre's plenty of theory on how to do these if you fancy reading around, that's probably the way to find the fastest approach...

PostPosted: Fri Nov 25, 2005 10:52 am
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spugmeistress
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Joined: 22 Feb 2005
Posts: 460
Location: manchester, uk

 		Re: #173-purple-circle set-the 14-15 puzzle
chichiri wrote:

see card catalog


as far as i can see there isnt an image up on the card catalog, and it doesnt seem you can do the puzzle without it, so if anyone could get an image for those of us without the cards, thatd be nice :)

rach =)

PostPosted: Fri Nov 25, 2005 7:43 pm
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Hunting4Treasure
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Joined: 06 Aug 2005
Posts: 385
Location: Tampa Bay Area, FL USA

 		Until someone can get an image up, the tiles are placed like this:

Code:

 1   2   3   4
 5   6   7   8
 9  10  11  12
13  15  14   *

*empty space
'13 15 14' isn't a typo

I've found a solution for successfully switching 15 and 14 into their proper spaces, but it leaves the blank in a different spot... *not* in the upper left spot. From what I've read in research, it's *impossible* to place them correctly and have the blank in the bottom right corner. Shocked

I didn't know what they were asking before now, so I'll have to research further to find a solution placing the blank in the upper left corner. Confused
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PostPosted: Fri Nov 25, 2005 11:35 pm
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Wowbagger
Boot


Joined: 22 Aug 2005
Posts: 69
Location: Leafy Surrey, UK

 		Here you go guys, as I'm having a scanning frenzy today...
14-15-[back].jpg
 Description   
 Filesize   20.16KB
 Viewed   267 Time(s)

14-15-[back].jpg
14-15.jpg
 Description   
 Filesize   20.28KB
 Viewed   323 Time(s)

14-15.jpg

PostPosted: Sat Nov 26, 2005 1:39 pm
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kksweety
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Joined: 14 May 2005
Posts: 103
Location: Liverpool UK

 		insoluble??
ok, found this website...

http://www.mathematische-basteleien.de/15puzzle.htm

which says:

Spoiler (Rollover to View):

found an insoluble 15puzzle in Italy, where the numbers 14 und 15 are changed.
The puzzle in this order was a big seller in the 19th century. The inventor Sam Lloyd offered $1,000 for a solution. This puzzle is unsolvable. The permutation (1,2,...,13,15,14) is odd because of the pair (15,14). You can't change it by sliding to the even permutation (1,2,...,13,14,15).

I thought that it was intention to make the puzzle insoluble. Now in August 2004 Martin Beckenkamp sent me an email that a 15puzzle is installed at his handy [England: mobile (phone), USA: cell (phone) Wink] and shows "solved", if the numbers have this order
01 02 03 __
04 05 06 07
08 09 10 11
12 13 14 15
You can reach this order with the Italian puzzle above, where 14 and 15 are changed.


PostPosted: Mon Nov 28, 2005 12:39 pm
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kksweety
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Joined: 14 May 2005
Posts: 103
Location: Liverpool UK

 		also found this if it helps
http://www.cut-the-knot.com/pythagoras/fifteen.shtml

PostPosted: Mon Nov 28, 2005 12:53 pm
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cronogenesis
Decorated


Joined: 02 Jun 2005
Posts: 201
Location: Notts UK

 		Theres a solve on the card.

Spoiler (Rollover to View):
14 11 12 8 7 6 10 12 8 7 4 3 6 4 7 14 11 15 13 9 12 8 4 10 8 4 14 11 15 13 9 12 4 8 5 4 8 9 13 14 10 6 2 1


And make sure yer say thanks Very Happy
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PostPosted: Mon Nov 28, 2005 2:58 pm
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Nightingale
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 		Cronogenesis, bloody good work - that man(or woman)!

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PostPosted: Mon Nov 28, 2005 3:45 pm
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cronogenesis
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 		Its 15 year old male gaint actually Very Happy
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PostPosted: Mon Nov 28, 2005 3:58 pm
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Langley Moor
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Joined: 27 Oct 2005
Posts: 86

 		Well done on that one, was getting close but couldn't get it quite as efficient as that... now there's only the yellows, which are harder than this due to the number of possible answers! Rolling Eyes

PostPosted: Mon Nov 28, 2005 4:10 pm
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Nightingale
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 		Bloody good solve that 15 year old male giant then!

Laughing

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PostPosted: Mon Nov 28, 2005 4:11 pm
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uneasyjd
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 		Thank you thank you thank you!
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PostPosted: Tue Nov 29, 2005 12:18 am
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jamesi
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Joined: 25 Sep 2002
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 		thanks a bunch cronogenesis, for allowing me to sleep tonight Very Happy
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PostPosted: Fri Dec 09, 2005 1:39 am
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simonfr
Kilroy

Joined: 16 Dec 2005
Posts: 1

 		I'm a bit confused by the instructions. (This is also my first post here, so I apologise if the use of spoiler space is inappropriate)

"What is the shortest way to move the tiles in order to get the vacant square from the bottom right to the top left corner and to swap the 14 and 15 tiles?"

Spoiler (Rollover to View):

Does this mean that the rest of the tiles have to be in order? I infer that from some of the posts here, but the card doesn't mention that requirement - could the rest of the numbers be in any position as long as the blank is in the top left, 15 is in 14's original position, and vice versa?


PostPosted: Fri Dec 16, 2005 9:15 am
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