When you rearrange the letters in the word "NO" in all possible ways you have NO ON These are both English dictionary words. Are there any 3 letter words where all 6 of the 3 letter permutations of its letters are also all words? For example, TEA rearranges to TEA TAE ETA EAT ATE AET. But, of course, not all of these are dictionary words!
I wrote a Python script which checks for the existence of these words - I couldn't find any.
import itertools words =  with open('dictionary.txt') as f: for line in f: if len(line.strip()) == 3: words += [line.strip().lower()] def winner(word): global words with open('words.txt') as file: for combo in itertools.permutations(word,len(word)): if not ''.join(combo) in words: return False return True for word in words: if(winner(word)): print(word)
If someone wants to try with a bigger dictionary than mine, go ahead!
Edit: Based upon the Scrabble dictionary VictorHenry has provided, there are four such sets of words:
However, the validity of these 'words' is left for the reader to decide :)
Apparently the word "EEW" was just added to the fifth edition of the OSPD which is the Official Scrabble Players Dictionary. It is, as you would expect, an expression of disgust ("eew gross!")
Of course, EEW can be anagrammed to WEE and EWE, both of which are also words.
ZZZ (already suggested by valuable_asset) is also an acceptable Scrabble word in that edition of the OSPD.
I was going to write a Python program, but Tryth has already done so. That being said, Tryth, you might want to use this list of 3-letter Scrabble words for your program and see if you have any better luck.
Edit: Apparently HOO, OHO, and OOH are all words in that dictionary as well.