## Highest percentage of words from a set of letters?

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woleeri
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### Highest percentage of words from a set of letters?

Rules is:
• letters must form one english word
• punctuation in that word can be ignored (AINT, SO-SO
• only count unique permutations (only three ways to permutate letters of ALL)

With 2 letters, we can get 100%
eg ON gives us words for all unique permutations:
[/ON /NO]
[english words are marked with a slash]

With three letters, can we get 50%?
Spoiler:
Yes - easy:
AET gives us 50%
[AET /ATE /TEA TAE /EAT ETA]

With three letters, can we get 66.7%?
Spoiler:
EEW give us 66.7%:
[EEW /EWE /WEE]

With three letters can you do better?

With four letters, can we get above 25%?
Spoiler:
(I’ll offer OPST as a highish scorer).

With five letters, can we get above 15%?
Spoiler:
the answer may surprise you

Good luck!

skeptical scientist
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### Re: Highest percentage of words from a set of letters?

4 letters:
Spoiler:
AEST:
Of the 24 permutations, words include east, eats, etas (multiple instances of the greek letter eta), sate, seat, seta (a stiff hair or bristle), and tase (shoot someone with a taser), for a total of 7, or 29%. I think that outscores OPST, which I can only think of 5 anagrams for.
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Buttons
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### Re: Highest percentage of words from a set of letters?

We might need some clarification on what constitutes an English word. Pick a Scrabble dictionary, say?

If we're just confining ourselves to any old dictionary, then
Spoiler:
WWW
has a pretty good percentage for three letters. I think I can prove it's optimal.

SS:
Spoiler:
OPST has six: opts, post, pots, spot, stop, tops. But AEST has nine according to SOWPODS: ates, east, eats, etas, sate, seat, seta, taes, teas.

bpsp
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### Re: Highest percentage of words from a set of letters?

Non-constructive thought:

Spoiler:
Some of these can be cheesed by loading a word with a small number of letters. For example, 25% can be matched with 4 letters by things like 'sass' and 'epee', as they only have 4 distinct permutations. Though these are beaten by skeptical's 'aest'.

However, I bet that one of 'aaaa', 'eeee', 'zzzz', or 'oooo' can be found in most dictionaries, which gives an undeserved 100%

For 5-letter words, it seems that there should be some word with the construction aabaa for some letters a and b, which would give an easy 20%. At the least, I'd imagine 'ooooh' or 'aaaah' would be acceptable words to some people.

For 6-letter words, booboo, at 7% if I did my math correctly, seems like it would be ahead for now.

JBJ
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### Re: Highest percentage of words from a set of letters?

50% on 4 letters
Spoiler:
(OOTT)
OOTT OTOT OTTO TTOO TOOT TOTO

Edit:
Spoiler:
3 letters
ADN = 83% if we allow acronyms
ADN AND DAN DNA NDA=(Non Disclosure Agreement) NAD=(Nicotinamide Adenine Dinucleotide)
Last edited by JBJ on Wed Jul 29, 2009 5:16 pm UTC, edited 1 time in total.
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Oculus Vespertilionis
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### Re: Highest percentage of words from a set of letters?

I'm interested in to what extent the results here will be very different with English than with another language. I would expect that a language with greater phonemic regularity, like Spanish, would also have greater density of use from letter sets.
I also speculated that a highly regular constructed language like Lojban might have very high percentages, but because of Lojban's rigid rules about consonant and verb order, there are likely fewer anagrams there.
-OcV
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Qaanol
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### Re: Highest percentage of words from a set of letters?

3 letters has 100%
Spoiler:
OOH/HOO/OHO
(all interjections/onomatopoeia)

5 letters has 10/120 for 8.3%
Spoiler:
least, lates, salet, slate, stale, steal, stela, tales, teals, tesla

I must admit I've never thought to pursue highest-percentage before. I've often thought about highest number of words from a set of letters though.
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Macbi
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### Re: Highest percentage of words from a set of letters?

Qaanol wrote:3 letters has 100%
Spoiler:
OOH/HOO/OHO
(all interjections/onomatopoeia)

5 letters has 10/120 for 8.3%
Spoiler:
least, lates, salet, slate, stale, steal, stela, tales, teals, tesla

I must admit I've never thought to pursue highest-percentage before. I've often thought about highest number of words from a set of letters though.

five letters 12/120 for 10%
Spoiler:
"Spear", though I can't remember all the anagrams.
I had a python script a while ago for finding the most anagrammable word. "Spear" came out top with 12 anagrams (including "spea"r) second and third were and "stelar" and "stela" with 11 and 10 each. I was using the Scrabble dictionary. If I can find the script I'll tell you what the all the anagrams were were.
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Buttons
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### Re: Highest percentage of words from a set of letters?

skeptical scientist
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### Re: Highest percentage of words from a set of letters?

Buttons wrote:SS:
Spoiler:
OPST has six: opts, post, pots, spot, stop, tops. But AEST has nine according to SOWPODS: ates, east, eats, etas, sate, seat, seta, taes, teas.

Spoiler:
Oops, I didn't think of "opts", and for some reason my anagram generator didn't either. Also, I know I had "teas" on my list; I'm not sure how it disappeared from my post, but it clearly disappeared before I counted. So I'll claim eight anagrams for AEST, or 33%.

Other than that, I'm not impressed with your word list. "Tase" is definitely a word, and in common usage no less (e.g. "Don't tase me bro"); it also makes several major online dictionaries, including Merriam-Webster, The Free Dictionary, and Wiktionary. I'm not sure how "ates" makes it as a word; it is ostensibly the plural of [url=org/wiki/Ate]Ate[/url], a Greek goddess, and as such I don't see why it isn't capitalized, and how it can be pluralized. I suppose perhaps it could be used as a synonym for ruin, but that definition doesn't seem to appear anywhere that I could find. Also, "taes" doesn't seem to exist except as a "valid word in this word list" - a definition is not to be found anywhere (at least not by Google), so if it's a word, it's useless for everything besides scrabble. Perhaps it's a plural for "tae", which merriam-webster.com at least thinks is a word, even if it won't tell me what it is without a credit card. (By the way, if you allow "tae" as a word, then AET gets 5 anagrams: ate, eat, eta, tae, and tea, for a total of 83%, beating your "eew". Also, going off bpsp's idea, "zzz" makes SOWPODS, for 100%.)

I prefer my judge my words by actual word-ness, rather than appearance in some scrabble dictionary, but I suppose I can see the merit in having a single fixed word list for this puzzle. I just wish it didn't strike me as so arbitrary and wrong...

JBJ: No acronyms. Also,
Spoiler:
I'm not sure how you justify "toto" and "otto" as words, but if you can provide links I'll reconsider.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

Lord Aurora
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### Re: Highest percentage of words from a set of letters?

skeptical scientist wrote:JBJ: No acronyms. Also,
Spoiler:
I'm not sure how you justify "toto" and "otto" as words, but if you can provide links I'll reconsider.

Spoiler:
Both reasonably common names (Toto being the dog in Wizard of Oz, Otto being the name of several German bigwigs). But yeah, not sure they count as words, per se.
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Qaanol
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### Re: Highest percentage of words from a set of letters?

wee free kings

JBJ
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### Re: Highest percentage of words from a set of letters?

@macbi - here's the 12 anagrams
Spoiler:
apers apres asper pares parse pears prase presa rapes reaps spare spear
According to this word list: http://www.math.toronto.edu/jjchew/scra ... mon-5.html

For 5 letters 11.7%
Spoiler:
ester reest reset steer stere terse trees
Same word list source: http://www.math.toronto.edu/jjchew/scra ... mon-5.html

loops was a close second with 8.3%
loops polos pools sloop spool
Last edited by JBJ on Thu Jul 30, 2009 6:24 pm UTC, edited 1 time in total.
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Qaanol
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### Re: Highest percentage of words from a set of letters?

JBJ wrote:@macbi - here's the 12 anagrams
Spoiler:
apers apres asper pares parse pears prase presa rapes reaps spare spear
According to this word list: http://www.math.toronto.edu/jjchew/scra ... mon-5.html

For 5 letters 17.5%
Spoiler:
ester reest reset steer stere terse trees
Same word list source: http://www.math.toronto.edu/jjchew/scra ... mon-5.html

loops was a close second with 12.5%
loops polos pools sloop spool

5 letters containing one pair of duplicates has 60 distinct permutations. So 5/60 = 8.3% and 7/60 = 11.7%. Which is to say, excellent find!
wee free kings

JBJ
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### Re: Highest percentage of words from a set of letters?

Qaanol wrote:5 letters containing one pair of duplicates has 60 distinct permutations. So 5/60 = 8.3% and 7/60 = 11.7%. Which is to say, excellent find!

Sorry, bad maths on my part. For some reason I came up with 40 permutations...
I've edited my previous post.
So, you sacked the cocky khaki Kicky Sack sock plucker?
The second cocky khaki Kicky Sack sock plucker I've sacked since the sixth sitting sheet slitter got sick.

woleeri
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### Re: Highest percentage of words from a set of letters?

Excellent responses, thanks.

I found the same five letters as JBJ, but with 9 or arguably 10 words, making 15% or 16.7%
Spoiler:
EESTR
S0WP0DS2 gives:
ester, reest, reset, retes, steer, stere, teers, teres, terse, trees

Not sure about TEERS

The rest seem legitimate, if occasionally obscure words.

Wonder what percentage we'd get if extended (without regarding accents) to all the official languages of the EU?

Best I've got for 6 letters is 5%, if we allow a few scrabble-only words. Otherwise, it is hard to get above 3%
Spoiler:
aeprss

Qaanol
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### Re: Highest percentage of words from a set of letters?

woleeri wrote:Excellent responses, thanks.

I found the same five letters as JBJ, but with 9 or arguably 10 words, making 15% or 16.7%
Spoiler:
EESTR
S0WP0DS2 gives:
ester, reest, reset, retes, steer, stere, teers, teres, terse, trees

Not sure about TEERS

The rest seem legitimate, if occasionally obscure words.

Neither RETES nor TEERS appear on merriam-webster.com, so that's 8/60 = 13.3%
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jestingrabbit
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### Re: Highest percentage of words from a set of letters?

Qaanol wrote:
woleeri wrote:Excellent responses, thanks.

I found the same five letters as JBJ, but with 9 or arguably 10 words, making 15% or 16.7%
Spoiler:
EESTR
S0WP0DS2 gives:
ester, reest, reset, retes, steer, stere, teers, teres, terse, trees

Not sure about TEERS

The rest seem legitimate, if occasionally obscure words.

Neither RETES nor TEERS appear on merriam-webster.com, so that's 8/60 = 13.3%

Your choice of dictionary isn't definitive. This is where the problem lies with puzzles like this: there is a subjective element that cannot be eliminated.
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