Multiple Anagrams
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Multiple Anagrams
Whenever I see the word STOP, painted on the road or on a sign or whatever, I always think about how it's cool how many anagrams it has - OPTS POST POTS STOP SPOT and TOPS - 6 in total (unless I've missed some obscure stuff I don't know about).
When I was lying in bed last night I was thinking about this, and wondering how well we could do in finding words with the most anagrams.
A brief bit of maths - an N letter word where all its letters are different will have N! (N x N-1 x N-2 and so on down to 1) possible permutations of its letters. So for a 4 letter word like STOP there are 4 x 3 x 2 x1 = 24 ways you can arrange the letters. So STOP, with 6 anagrams, manages 6/24 = 0.25 on the Raccoon Anagram Coolness Coefficient Of Niceness score.
At the moment the best I can manage for 3 letters is TEA (ATE/EAT/ETA/TEA = 4/6).
Of course, if you have repeated letters this reduces the number of possible permutations, so POOP scores 1/6 since there are only 6 ways you can distinctly arrange 2 pairs of letters.
Does that makes sense? Yes? Great. What's the best score you can manage? How can we do on the higher words?
When I was lying in bed last night I was thinking about this, and wondering how well we could do in finding words with the most anagrams.
A brief bit of maths - an N letter word where all its letters are different will have N! (N x N-1 x N-2 and so on down to 1) possible permutations of its letters. So for a 4 letter word like STOP there are 4 x 3 x 2 x1 = 24 ways you can arrange the letters. So STOP, with 6 anagrams, manages 6/24 = 0.25 on the Raccoon Anagram Coolness Coefficient Of Niceness score.
At the moment the best I can manage for 3 letters is TEA (ATE/EAT/ETA/TEA = 4/6).
Of course, if you have repeated letters this reduces the number of possible permutations, so POOP scores 1/6 since there are only 6 ways you can distinctly arrange 2 pairs of letters.
Does that makes sense? Yes? Great. What's the best score you can manage? How can we do on the higher words?
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Re: Multiple Anagrams
I would guess that the best you can do slides down fairly quickly with word length. There are no nines with more than 4 anagrams (REACTIONS/CREATIONS/ACTIONERS/NARCOTISE) although there are some with a lot of redundant letters (SONGOLOLO) which will have a higher ratio.
I'll try to think of some good examples later, and then at some point I'll work it out proper-like (unless someone else does it first.)
I'll try to think of some good examples later, and then at some point I'll work it out proper-like (unless someone else does it first.)
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Re: Multiple Anagrams
SILENT is quite a good 6, with five valid anagrams (SILENT, ENLIST, TINSEL, INLETS and LISTEN).
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Re: Multiple Anagrams
When I did my Lattice (for another thread) I came across the word DETAINS, which has a total of 7 anagrams: DESTAIN, DETAINS, INSTEAD, SAINTED, SATINED, STAINED and TIENDAS.
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Re: Multiple Anagrams
In Scrabble the racks RETAINS and ANGRIEST are notorious but I'm not sure how many of the words are Countdown valid. And again I'm too lazy to check.
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Re: Multiple Anagrams
Lexplorer is your friend:Charlie Reams wrote:In Scrabble the racks RETAINS and ANGRIEST are notorious but I'm not sure how many of the words are Countdown valid. And again I'm too lazy to check.
- ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
- ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST (5)
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Re: Multiple Anagrams
Phil Reynolds wrote:Lexplorer is your friend:Charlie Reams wrote:In Scrabble the racks RETAINS and ANGRIEST are notorious but I'm not sure how many of the words are Countdown valid. And again I'm too lazy to check.
- ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
- ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST, GRANITES (6)
16/10/2007 - Episode 4460
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Dinos Sfyris 76 - 78 Dorian Lidell
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Re: Multiple Anagrams
As Phil correctly pointed out, Lexplorer is your friend.Kai Laddiman wrote:Phil Reynolds wrote:Lexplorer is your friend:Charlie Reams wrote:In Scrabble the racks RETAINS and ANGRIEST are notorious but I'm not sure how many of the words are Countdown valid. And again I'm too lazy to check.
- ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
- ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST, GRANITES (6)
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Re: Multiple Anagrams
Lexplorer is not definitive, Jimdic makes some fairly arbitary decisions on mass noun plurals.
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Re: Multiple Anagrams
[quote="Charlie Reams"]I would guess that the best you can do slides down fairly quickly with word length. There are no nines with more than 4 anagrams (REACTIONS/CREATIONS/ACTIONERS/NARCOTISE)
This is a very eerie coincidence as whilst I was walking in the countryside with my wife this afternoon I was trying to think which combination of letters gives the most 9-letter words and and I get home to read this thread.
My conclusion was that this combination, which came up in the game between myself and Charlie on CD, was probably close the maximum possible.
I was also thinking of 8-letter anagrams that could be derived from the multiple anagrams NOTARISED and ORDINATES, such as STRAINED, DETRAINS, RATIONED, SEDATION.
Us CD'ers really should get out more! Oh yes! I was out wasn't I. No hope really is there
This is a very eerie coincidence as whilst I was walking in the countryside with my wife this afternoon I was trying to think which combination of letters gives the most 9-letter words and and I get home to read this thread.
My conclusion was that this combination, which came up in the game between myself and Charlie on CD, was probably close the maximum possible.
I was also thinking of 8-letter anagrams that could be derived from the multiple anagrams NOTARISED and ORDINATES, such as STRAINED, DETRAINS, RATIONED, SEDATION.
Us CD'ers really should get out more! Oh yes! I was out wasn't I. No hope really is there
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Re: Multiple Anagrams
A scores 1.0 on the Raccoon scale. What do I win?
Re: Multiple Anagrams
OPPO. That makes 2/6.Michael Wallace wrote:Of course, if you have repeated letters this reduces the number of possible permutations, so POOP scores 1/6 since there are only 6 ways you can distinctly arrange 2 pairs of letters.
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Re: Multiple Anagrams
Aha, good workDavid Roe wrote:OPPO. That makes 2/6.Michael Wallace wrote:Of course, if you have repeated letters this reduces the number of possible permutations, so POOP scores 1/6 since there are only 6 ways you can distinctly arrange 2 pairs of letters.
You win whatever is in the Mystery Box.Dinos Sfyris wrote:A scores 1.0 on the Raccoon scale. What do I win?
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Re: Multiple Anagrams
DERATIONS is another 9 you can have as wellAllan Harmer wrote:I was also thinking of 8-letter anagrams that could be derived from the multiple anagrams NOTARISED and ORDINATES, such as STRAINED, DETRAINS, RATIONED, SEDATION.
Using Lexplorer (although it is not definitive), it comes up with fourteen 8's:
NOTARIES, NOTARISE, SENORITA, INTRADOS, ASTEROID, DETRAINS, RANDIEST, STRAINED, SEDATION, DERATION, ORDINATE, RATIONED, ANEROIDS and ANODISER.
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Re: Multiple Anagrams
Plates has long been one of my favourites for this:
PALEST
PASTEL
PETALS
PLATES
PLEATS
SEPTAL
STAPLE
TEPALS
So that would be 7/720 would it? (6!= 720).
It would be interesting to have a list of all the quad-nines, I came up with with, with a bit of help from Google:
ACTIONERS, CREATIONS, NARCOTISE, REACTIONS
INSETTERS, INTERESTS, STERNITES, TRITENESS
RESTRAINS, STRAINERS, TARRINESS, TRANSIRES
RATTINESS, RESISTANT, STRAITENS, TARTINESS
INTERLAPS, STRAPLINE, TRAPLINES, TRIPLANES
PALEST
PASTEL
PETALS
PLATES
PLEATS
SEPTAL
STAPLE
TEPALS
So that would be 7/720 would it? (6!= 720).
It would be interesting to have a list of all the quad-nines, I came up with with, with a bit of help from Google:
ACTIONERS, CREATIONS, NARCOTISE, REACTIONS
INSETTERS, INTERESTS, STERNITES, TRITENESS
RESTRAINS, STRAINERS, TARRINESS, TRANSIRES
RATTINESS, RESISTANT, STRAITENS, TARTINESS
INTERLAPS, STRAPLINE, TRAPLINES, TRIPLANES
Last edited by Martin Gardner on Tue Feb 24, 2009 2:52 pm, edited 1 time in total.
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Re: Multiple Anagrams
When I was designing my word lists for my Countdown Book, I started to do this and got the exact same 5 quads as you've posted (I also had 51 triplet anagrams and 223 doublet anagrams).Martin Gardner wrote:It would be interesting to have a list of all the quad-nines, I can up with with, with a bit of help from Google:
ACTIONERS, CREATIONS, NARCOTISE, REACTIONS
INSETTERS, INTERESTS, STERNITES, TRITENESS
RESTRAINS, STRAINERS, TARRINESS, TRANSIRES
RATTINESS, RESISTANT, STRAITENS, TARTINESS
INTERLAPS, STRAPLINE, TRAPLINES, TRIPLANES
There must be a simple way to work out all the anagram sets of 2, 3 and 4 anagrams.
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Re: Multiple Anagrams
That's poor. There are loads of 2-letter words that get a score of 1.0 which is clearly more impressive. The list starts Aa, Ab, Ad, etc... depending on which dictionary you use. (If you want to use 'common' words only, then there's still At, On, and many others).Dinos Sfyris wrote:A scores 1.0 on the Raccoon scale. What do I win?
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Re: Multiple Anagrams
The INTERESTS one does pretty well having three doubles.Martin Gardner wrote:Plates has long been one of my favourites for this:
PALEST
PASTEL
PETALS
PLATES
PLEATS
SEPTAL
STAPLE
TEPALS
So that would be 7/720 would it? (6!= 720).
It would be interesting to have a list of all the quad-nines, I came up with with, with a bit of help from Google:
ACTIONERS, CREATIONS, NARCOTISE, REACTIONS
INSETTERS, INTERESTS, STERNITES, TRITENESS
RESTRAINS, STRAINERS, TARRINESS, TRANSIRES
RATTINESS, RESISTANT, STRAITENS, TARTINESS
INTERLAPS, STRAPLINE, TRAPLINES, TRIPLANES
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Re: Multiple Anagrams
Maybe we could come up with a more complex scoring system to take this into account. But you can do that.Charlie Reams wrote:I would guess that the best you can do slides down fairly quickly with word length.
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Re: Multiple Anagrams
Perhaps you could times the Raccoon score as it stands now by some constant to the power of n, where n is the number of letters. For example DEIFIED (which is cool cos its palindromic) also has the anagaram EDIFIED and its score by the current Raccoon system is:Gavin Chipper wrote:Maybe we could come up with a more complex scoring system to take this into account. But you can do that.Charlie Reams wrote:I would guess that the best you can do slides down fairly quickly with word length.
2 x 2! x 2! x 2! / 7! = an unimpressive 1/315
but if we timesed it by say 2^7 or 3^7 it'd have 128/315 or 243/35 which is a bit more of a respectable score given the length of the word.
edit: actually somewhere between these 2 values would be good, perhaps e?
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Re: Multiple Anagrams
ZZZ is pretty much unbeatable, then. Or in French you can have MMM.Neil Zussman wrote:That's poor. There are loads of 2-letter words that get a score of 1.0 which is clearly more impressive. The list starts Aa, Ab, Ad, etc... depending on which dictionary you use. (If you want to use 'common' words only, then there's still At, On, and many others).Dinos Sfyris wrote:A scores 1.0 on the Raccoon scale. What do I win?
If you cut a gandiseeg in half, do you get two gandiseegs or two halves of a gandiseeg?
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Re: Multiple Anagrams
There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.Martin Gardner wrote:ZZZ is pretty much unbeatable, then. Or in French you can have MMM.Neil Zussman wrote:That's poor. There are loads of 2-letter words that get a score of 1.0 which is clearly more impressive. The list starts Aa, Ab, Ad, etc... depending on which dictionary you use. (If you want to use 'common' words only, then there's still At, On, and many others).Dinos Sfyris wrote:A scores 1.0 on the Raccoon scale. What do I win?
Last edited by Joseph Bolas on Thu Feb 26, 2009 4:29 pm, edited 1 time in total.
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Re: Multiple Anagrams
Yes but GRRRL only scores 0.05 on the raccoon scale as only 3!/5! of its constructions make the word GRRRL which is its only anagramJoseph Bolas wrote:There is actually a few words, that you can play in Countdown that have three consequitive R's, which are GRRRLS, GRRRL and BRRR.
Re: Multiple Anagrams
Consequitive?
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Re: Multiple Anagrams
I wasn't quite sure what the score would've been for them (otherwise I would've included it in the post ).Dinos Sfyris wrote:Yes but GRRRL only scores 0.05 on the raccoon scale as only 3!/5! of its constructions make the word GRRRL which is its only anagramJoseph Bolas wrote:There is actually a few words, that you can play in Countdown that have three consequitive R's, which are GRRRLS, GRRRL and BRRR.
I did mean consecutive.Jon Corby wrote:Consequitive?
Last edited by Joseph Bolas on Thu Feb 26, 2009 5:18 pm, edited 1 time in total.
Re: Multiple Anagrams
Consecuitive?
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Re: Multiple Anagrams
Hmm, ZZZ is not a legal word accorind to the Scrabble word list I have. In fact no 3 letter-word scores 1.0 on the scale. So my 2 letter suggestions are unbeatable (Although I'm sure Craig or someone can correct me if my list is outdated).Martin Gardner wrote:ZZZ is pretty much unbeatable, then. Or in French you can have MMM.Neil Zussman wrote:That's poor. There are loads of 2-letter words that get a score of 1.0 which is clearly more impressive. The list starts Aa, Ab, Ad, etc... depending on which dictionary you use. (If you want to use 'common' words only, then there's still At, On, and many others).Dinos Sfyris wrote:A scores 1.0 on the Raccoon scale. What do I win?
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Re: Multiple Anagrams
Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!Neil Zussman wrote:Hmm, ZZZ is not a legal word accorind to the Scrabble word list I have... Although I'm sure Craig or someone can correct me if my list is outdated).
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Re: Multiple Anagrams
That would be the ultimate waste of 2 blanks...Ben Wilson wrote:Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!Neil Zussman wrote:Hmm, ZZZ is not a legal word accorind to the Scrabble word list I have... Although I'm sure Craig or someone can correct me if my list is outdated).
Incidentally, I don't suppose you know of any website with an up-to-date printer-friendly list of valid 2 and 3 letter words do you? I found one several years ago which I use for friendly games with my parents, but we could do with a new one.
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Re: Multiple Anagrams
What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?Joseph Bolas wrote: There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.
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Re: Multiple Anagrams
Presumably it's what a lion calls a bunch of young ladies.Adam Dexter wrote:What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?Joseph Bolas wrote: There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.
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Re: Multiple Anagrams
OK I've found it... but I would like to question whether it would be allowed as it's only seen with Riot preceding it. I thought the rule was that if it was only seen as part of a phrase, then it wasn't allowed? Some types of acid I think are an example... but I can't think of any.
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Re: Multiple Anagrams
Oxalic.Adam Dexter wrote:I thought the rule was that if it was only seen as part of a phrase, then it wasn't allowed? Some types of acid I think are an example... but I can't think of any.
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Re: Multiple Anagrams
What's the be-all-and-almost-end-all for checking word validity for Countdown?Phil Reynolds wrote:Oxalic.Adam Dexter wrote:I thought the rule was that if it was only seen as part of a phrase, then it wasn't allowed? Some types of acid I think are an example... but I can't think of any.
If OXALIC is good, it's not in the stemmer. Nor is it specified in that askoxford.com link you posted before Phil.
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Re: Multiple Anagrams
I'd've thought the absolute 'be all and end all' would be Susie. Failing that your own ODE2r (if you can be bothered to get one). The stemmer is probably pretty good - but I presume OXALIC isn't in because Phil was giving it as an example of a word that only appears in combination (I could be wrong, but my dictionary is on the other side of the room and I can't be bothered to check (it's not a big room, I'm just lazy)).Matt Morrison wrote:What's the be-all-and-almost-end-all for checking word validity for Countdown?
If OXALIC is good, it's not in the stemmer. Nor is it specified in that askoxford.com link you posted before Phil.
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Re: Multiple Anagrams
It isn't good. That's why I posted it, you moron.Matt Morrison wrote:What's the be-all-and-almost-end-all for checking word validity for Countdown?Phil Reynolds wrote:Oxalic.Adam Dexter wrote:I thought the rule was that if it was only seen as part of a phrase, then it wasn't allowed? Some types of acid I think are an example... but I can't think of any.
If OXALIC is good, it's not in the stemmer. Nor is it specified in that askoxford.com link you posted before Phil.
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Re: Multiple Anagrams
GRRRL (noun) - a young woman regarded as independent and strong or aggressive, especially in her attitude to men or in her sexuality. It can also be spelt GRRL (and would assume that GRRLS would be allowed too).Michael Wallace wrote:Presumably it's what a lion calls a bunch of young ladies.Adam Dexter wrote:What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?Joseph Bolas wrote: There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.
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Re: Multiple Anagrams
You arse. I misread everything.Phil Reynolds wrote:It isn't good. That's why I posted it, you moron.Matt Morrison wrote:If OXALIC is good, it's not in the stemmer. Nor is it specified in that askoxford.com link you posted before Phil.
Any normal person would say something obvious from their school days like "hydrochloric" or "folic" but you just have to go and be special don't you Phil?
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Re: Multiple Anagrams
What's this? Disallowed words that only precede acid? Think we're in Dinos territory here. ETHANOIC is a good example as its 8 commonish letters, and has a valid anagram INCHOATE. Also a surprising word disallowed for this reason is BRASSED as you can only have BRASSED OFF.
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Re: Multiple Anagrams
I only knew about "oxalic" because it's bitten me on the bum before now.Matt Morrison wrote:Any normal person would say something obvious from their school days like "hydrochloric" or "folic" but you just have to go and be special don't you Phil?Phil Reynolds wrote:oxalic
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Re: Multiple Anagrams
Blimey, didn't know that one. One that puzzles me is WAISTED, which is allowed as it's listed as a derivative of WAIST; but whenever it comes up on the show, Susie always says, "as in high-waisted trousers" which seems to me like another instance of a word that's only used in combination. How would you use "waisted" as an adjective in its own right?Dinos Sfyris wrote:Also a surprising word disallowed for this reason is BRASSED as you can only have BRASSED OFF.
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Re: Multiple Anagrams
A total guess (more fun than looking it up) but perhaps "those trousers are waisted" might be fashion terminology for a particular type of waistband, perhaps ones that have a specially hemmed waistline as opposed to the waistband simply being the top of the trousers. Similar to the way that you might say "those shoes are heeled" - you'd only say that about high heels, despite the fact that of course all shoes have heels.Phil Reynolds wrote:Blimey, didn't know that one. One that puzzles me is WAISTED, which is allowed as it's listed as a derivative of WAIST; but whenever it comes up on the show, Susie always says, "as in high-waisted trousers" which seems to me like another instance of a word that's only used in combination. How would you use "waisted" as an adjective in its own right?Dinos Sfyris wrote:Also a surprising word disallowed for this reason is BRASSED as you can only have BRASSED OFF.
As such, you could then 'waist' (verb) some trousers by doing something to the wasteband, in a similar way that you can 'heel' shoes?
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Re: Multiple Anagrams
Haha, true story. On finding out that ZZZS had gone into the dictionary, I said if I picked up two blanks and an S I would definitely play it. The very next game, I did indeed have two blanks, an S and the Z but I chickened out and played BOOZERS instead.Ben Wilson wrote:Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!Neil Zussman wrote:Hmm, ZZZ is not a legal word accorind to the Scrabble word list I have... Although I'm sure Craig or someone can correct me if my list is outdated).
If you cut a gandiseeg in half, do you get two gandiseegs or two halves of a gandiseeg?
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Re: Multiple Anagrams
METRONOME is a good one. It has two other anagrams MONOMETER and MONOTREME, which you wouldn't necessarily expect from such a letter distribution, and 3 different repeated letters so its dinosified raccoon score is 3 x (2!)^3 x e^9/9! = 0.5359. Strangely though it only yields one 8: MOTORMEN.
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Re: Multiple Anagrams
This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.Dinos Sfyris wrote:METRONOME is a good one. It has two other anagrams MONOMETER and MONOTREME, which you wouldn't necessarily expect from such a letter distribution, and 3 different repeated letters so its dinosified raccoon score is 3 x (2!)^3 x e^9/9! = 0.5359. Strangely though it only yields one 8: MOTORMEN.
If you cut a gandiseeg in half, do you get two gandiseegs or two halves of a gandiseeg?
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Re: Multiple Anagrams
I can see the 9s but not the 8! Is this a sign that I'm good or shitMartin Gardner wrote:This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.Dinos Sfyris wrote:METRONOME is a good one. It has two other anagrams MONOMETER and MONOTREME, which you wouldn't necessarily expect from such a letter distribution, and 3 different repeated letters so its dinosified raccoon score is 3 x (2!)^3 x e^9/9! = 0.5359. Strangely though it only yields one 8: MOTORMEN.
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Re: Multiple Anagrams
LEPORINE, not a very common word, so I wouldn't worry. When watching this show for real, I got a seven.Dinos Sfyris wrote:I can see the 9s but not the 8! Is this a sign that I'm good or shitMartin Gardner wrote:This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.Dinos Sfyris wrote:METRONOME is a good one. It has two other anagrams MONOMETER and MONOTREME, which you wouldn't necessarily expect from such a letter distribution, and 3 different repeated letters so its dinosified raccoon score is 3 x (2!)^3 x e^9/9! = 0.5359. Strangely though it only yields one 8: MOTORMEN.
If you cut a gandiseeg in half, do you get two gandiseegs or two halves of a gandiseeg?