NO and ON has 100% anagrammability. ATE, TEA, and EAT has 50%. Anagrammability is the ratio between the number of letter reorderings that produce an anagram and the total number of possible letter orders. So NO has two possible letter NO and ON. Both are anagrams, therefore 2 / 2 = 1, 100%. ATE has 6 possible orderings (3!) - ATE, aet, TEA, tae, EAT, eta, 3 / 6 = half or 50%. In contrast CAN has no anagrammatic solutions, therefore 1 / 6 = 16.67%, which is the lowest percentage score possible for a 3 letter word. If no letters are repeated in the word, the equation for measuring anagrammability of a word is this: number of anagrammatic solutions / n! , where n = number of letters in a word. It is more complicated obviously for words with letter repititions like NOON. (See first comment below about calculating anagrammability with words / phrases with repeated letters.) Can you find other words that have more than one anagrammatic solution? And what word has the largest anagrammatic set (AS) ? (The AS for NO = 2, and EAT = 3.) The same measure for anagrammability goes for phrases as well.
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GUESS WHAT - THANKS BRIAN GRADY
The 4 anagrams below were 'found' by BRIAN GRADY (he 'made them up' but I use the word 'found' because each anagram is 'inherently' there in the possibilities of our language - much like new mathematical findings are inherent in numbers 0 - 9 and other underlying assumptions of maths.)
Guess What = Washes Gut = Hugest Saw = Huge Swats
IThe anagrammability of the above phrase is 4 / number of ways the letters 'guesswhat' can be ordered, which is[7!] x 36 . There are 36 different positions that 'ss' can be in the 9 spaces __ __ __ __ __ __ __ __ __. For any one positioning of the two 'ss's there are 7! orderings of the other 7 letters. Therefore the anagrammability of 'GUESS WHAT' =
4 / 181440 which is .000022
If there were only 2 anagrams the anagrammability would be .000011.
Of course, if there's more than 4 in the above AS then .000022 is incorrect.
Do you want to see if there is Brian?
Although...
You could cheat, doubling your Anagramibility by swapping two words round e.ge
Guess What = Washes Gut = Hugest Saw = Huge Swats=What Guess=Gut Washes=Saw Hugest=Swats Huge.
Also, I can see ones like
Wages Shut
Wages Huts
Wage Shuts
Washes Tug
And my personal favourite,
Sweats Hug
Lastly, Uncorrect is uncorrect.
Signed, Sealed, Pope General Caleb Benedictus XIII, Commander of the IVth Great and Bountiful Italian Empire.
CHEATING
I was going to accept word switching but no I don't think we can.
[1] it is trivial as it can always be done - so anagrammability will be measured from here on as not including simply changing the word order
[2] it is an operation on the word-level rather than the letter-level and so not really anagrammatic in spirit
So what is the word for where switching is at the word-level, ANALOGOS ?
And for phrases - ANAPHRASE. And how about switching two books in a library - ANATEXT ?
Can we have some ANALOGOS challenges? Can you analogomate a phrase so that it means the opposite of the original?
word & phrase switching
I guess one could categorise the anagrammatic treatment of a phrase:
1. word switching [ie., x! arrangements, where x is number of words]
2. letter switching within each word
here one would have two measures of anagrammability - for each
individual word and across words
3. letter switching between words
the number of possible positions here for any one word would be
y! - [z! -1], where y = number of letter position in whole phrase
and z = number of letter positions in word that target letter has
come from
This may be a bit simplistic but the right idea. Of course, if you had a couple of phrases one could switch at the phrase level as well.
A second issue is meaningfulness - this shouldn't be an issue with 1 word
but could be with 2 [even though Caleb's word switches above do seem coherent] but when you get to phrases a high proportion of word / phrase switches would render the text incoherent.
Hence one could limit allowed switches to only those anagrams for which the resultant word / phrase is meaningful [but not necessarily topic-related]