Multiple Anagrams

[Michael Wallace]

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?

[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) 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.)

[Phil Reynolds]

SILENT is quite a good 6, with five valid anagrams (SILENT, ENLIST, TINSEL, INLETS and LISTEN).

[Joseph Bolas]

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.

[Charlie Reams]

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.

[Phil Reynolds]

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.

Lexplorer is your friend:

• ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
• ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST (5)

[Kai Laddiman]

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.

Lexplorer is your friend:

• ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
• ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST, GRANITES (6)

[Matt Morrison]

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.

Lexplorer is your friend:

• ANTSIER, NASTIER, RETAINS, RETINAS, RETSINA, STAINER, STEARIN (7)
• ANGRIEST, GANISTER, GANTRIES, INGRATES, RANGIEST, GRANITES (6)

As Phil correctly pointed out, Lexplorer is your friend.

[Charlie Reams]

Lexplorer is not definitive, Jimdic makes some fairly arbitary decisions on mass noun plurals.

[Allan Harmer]

[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

[Dinos Sfyris]

A scores 1.0 on the Raccoon scale. What do I win?

[David Roe]

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.

OPPO. That makes 2/6.

[Michael Wallace]

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.

OPPO. That makes 2/6.

Aha, good work

A scores 1.0 on the Raccoon scale. What do I win?

You win whatever is in the Mystery Box.

[Joseph Bolas]

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.

DERATIONS is another 9 you can have as well

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.

[Martin Gardner]

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

[Joseph Bolas]

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

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).

There must be a simple way to work out all the anagram sets of 2, 3 and 4 anagrams.

[Neil Zussman]

A scores 1.0 on the Raccoon scale. What do I win?

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).

[Gavin Chipper]

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

The INTERESTS one does pretty well having three doubles.

[Gavin Chipper]

I would guess that the best you can do slides down fairly quickly with word length.

Maybe we could come up with a more complex scoring system to take this into account. But you can do that.

[Dinos Sfyris]

I would guess that the best you can do slides down fairly quickly with word length.

Maybe we could come up with a more complex scoring system to take this into account. But you can do that.

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:

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?

[Martin Gardner]

A scores 1.0 on the Raccoon scale. What do I win?

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).

ZZZ is pretty much unbeatable, then. Or in French you can have MMM.

[Joseph Bolas]

A scores 1.0 on the Raccoon scale. What do I win?

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).

ZZZ is pretty much unbeatable, then. Or in French you can have MMM.

There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.

[Dinos Sfyris]

There is actually a few words, that you can play in Countdown that have three consequitive R's, which are GRRRLS, GRRRL and BRRR.

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 anagram

[Jon Corby]

Consequitive?

[Joseph Bolas]

There is actually a few words, that you can play in Countdown that have three consequitive R's, which are GRRRLS, GRRRL and BRRR.

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 anagram

I wasn't quite sure what the score would've been for them (otherwise I would've included it in the post ).

Consequitive?

I did mean consecutive.

[Jon Corby]

Consecuitive?

[Neil Zussman]

A scores 1.0 on the Raccoon scale. What do I win?

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).

ZZZ is pretty much unbeatable, then. Or in French you can have MMM.

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).

[Ben Wilson]

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).

Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!

[Neil Zussman]

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).

Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!

That would be the ultimate waste of 2 blanks...
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.

[Adam Dexter]

There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.

What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?

[Michael Wallace]

There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.

What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?

Presumably it's what a lion calls a bunch of young ladies.

[Adam Dexter]

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.

[Phil Reynolds]

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.

Oxalic.

[Matt Morrison]

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.

Oxalic.

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.

[Michael Wallace]

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.

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)).

[Phil Reynolds]

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.

Oxalic.

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.

It isn't good. That's why I posted it, you moron.

[Joseph Bolas]

There is actually a few words, that you can play in Countdown that have three consecuitive R's, which are GRRRLS, GRRRL and BRRR.

What does GRRRLS mean? I've tried to look it up in my oed, but to no avail.. help?

Presumably it's what a lion calls a bunch of young ladies.

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).

[Matt Morrison]

If OXALIC is good, it's not in the stemmer. Nor is it specified in that askoxford.com link you posted before Phil.

It isn't good. That's why I posted it, you moron.

You arse. I misread everything.
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?

[Dinos Sfyris]

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.

[Phil Reynolds]

oxalic

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?

I only knew about "oxalic" because it's bitten me on the bum before now.

[Phil Reynolds]

Also a surprising word disallowed for this reason is BRASSED as you can only have BRASSED OFF.

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?

[Matt Morrison]

Also a surprising word disallowed for this reason is BRASSED as you can only have BRASSED OFF.

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?

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.

As such, you could then 'waist' (verb) some trousers by doing something to the wasteband, in a similar way that you can 'heel' shoes?

[Martin Gardner]

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).

Yep. ZZZ has been fine since May '07. Along with, comically, ZZZS. Possibly the most pointless words in the entire Scrabble lexicon!

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.

[Dinos Sfyris]

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.

[Martin Gardner]

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.

This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.

[Dinos Sfyris]

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.

This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.

I can see the 9s but not the 8! Is this a sign that I'm good or shit

[Martin Gardner]

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.

This game up a few months ago. EEIOLNPRT has the same property -three nines, only one eight.

I can see the 9s but not the 8! Is this a sign that I'm good or shit

LEPORINE, not a very common word, so I wouldn't worry. When watching this show for real, I got a seven.