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#209992 - 03/12/13 09:55 PM - - game for snowed-in winter entertainment  
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LukeJavan8 Offline
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Land of the Flat Water
Word Ladders

On Christmas Day 1877, assailed by two young ladies with “nothing to do,” Lewis Carroll invented a new “form of verbal torture”: Presented with two words of the same length, the solver must convert one to the other by changing a single letter at a time, with each step producing a valid English word. For example, HEAD can be converted to TAIL in five steps:

HEAD
HEAL
TEAL
TELL
TALL
TAIL

Carroll called the new pastime Doublets and published it in Vanity Fair, which hailed it as “so entirely novel and withal so interesting, that … the Doublets may be expected to become an occupation to the full as amusing as the guessing of the Double Acrostics has already proved.”

In some puzzles the number of steps is specified. In Nabokov’s Pale Fire, the narrator describes a friend who was addicted to “word golf.” “He would interrupt the flow of a prismatic conversation to indulge in this particular pastime, and naturally it would have been boorish of me to refuse playing with him. Some of my records are: HATE-LOVE in three, LASS-MALE in four, and LIVE-DEAD in five (with LEND in the middle).” I’ve been able to solve the first two of these fairly easily, but not the last.

But even without such a constraint, some transformations require a surprising number of steps. Carroll found that 10 were required to turn BLUE into PINK, and in 1968 wordplay expert Dmitri Borgmann declared himself unable to convert ABOVE into BELOW at all.

In a computer study of 5,757 five-letter English words, Donald Knuth found that most could be connected to one another, but 671 could not. One of these, fittingly, was ALOOF. In the wider English language, what proportion of words are “aloof,” words that cannot be connected to any of their fellows? Is ALOOF itself one of these?


----please, draw me a sheep----
#209994 - 03/12/13 11:49 PM Re: - - game for snowed-in winter entertainment [Re: LukeJavan8]  
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Buffalo Shrdlu Offline
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Vermont
LIVE
LINE
LEND
LEAD
DEAD

maybe?


formerly known as etaoin...
#209995 - 03/13/13 12:25 AM Re: - - game for snowed-in winter entertainment [Re: LukeJavan8]  
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jenny jenny Offline
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jenny jenny  Offline
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Lower Aberdeen, Mississippi
Look Luke! Four steps.
Wow! I must be quicker than Lewis Carroll. smile

HEAD
HEAL
HEIL
HAIL
TAIL

#209998 - 03/13/13 02:41 AM Re: - - game for snowed-in winter entertainment [Re: jenny jenny]  
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tsuwm Offline
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this too shall pass
yeahbut, strictly speaking, heil ain't English.

#209999 - 03/13/13 09:47 AM Re: - - game for snowed-in winter entertainment [Re: Buffalo Shrdlu]  
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Tromboniator Offline
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Alaska
Buff– LINE > LEND changes two letters.

I'm assuming that moving letters is illegal.

Does the starting word count as a step?

#210000 - 03/13/13 09:50 AM Re: - - game for snowed-in winter entertainment [Re: LukeJavan8]  
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Tromboniator Offline
old hand
Tromboniator  Offline
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Alaska
Won't let me edit. HEAD > TAIL example shows me that the starting word is not a step.

#210001 - 03/13/13 10:05 AM Re: - - game for snowed-in winter entertainment [Re: tsuwm]  
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jenny jenny Offline
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Originally Posted By: tsuwm
yeahbut, strictly speaking, heil ain't English.


yeahbut tsuwm , stricktly speaking, ain't ain't English, but what the heil. smile

#210003 - 03/13/13 12:05 PM Re: - - game for snowed-in winter entertainment [Re: Tromboniator]  
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Buffalo Shrdlu Offline
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Originally Posted By: Tromboniator
Buff– LINE > LEND changes two letters.

I'm assuming that moving letters is illegal.

Does the starting word count as a step?


Well, I wasn't sure about the moving letters thing, and I think the number of words and what constitutes a step is also unclear at this point. I was just going by "LIVE-DEAD in five (with LEND in the middle)" and if the initial word doesn't count then how can anything be in the middle?

ah well.


formerly known as etaoin...
#210004 - 03/13/13 12:07 PM Re: - - game for snowed-in winter entertainment [Re: LukeJavan8]  
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Buffalo Shrdlu Offline
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Buffalo Shrdlu  Offline
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Vermont
(and yes, as others have noticed, the Edit function seems to be messed up...)

> LINE > LEND changes two letters.

Well, it changes only one letter, but it does change the position of one of the three remaining.


formerly known as etaoin...
#210006 - 03/13/13 02:20 PM Re: - - game for snowed-in winter entertainment [Re: Buffalo Shrdlu]  
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LukeJavan8 Offline
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Land of the Flat Water
Wow!
I just found that in reading online. Glad it brought you all
a little fun. It is really. And my reply function does not
work on the immediate reply but if I back up 2-3 posts
it does work. Go figure. Enjoy.


----please, draw me a sheep----
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