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Word Game - Just for Fun

Years ago I invented a word game.  It involves the letters of a word and rearrangements.

The rule is: you start with a word, say like abc.  Then you rearrange by the rule
abc -> bca -> cab
All must be words.  Example:
tea -> eat -> ate
I could find only three such three-letter words, and one is a stretch.  The first is "tea," the second is "spa," and the third is "one." Therein lies the stretch: eon -> one -> neo.  "Neo" is kind of a word. 

I never could find a four letter word, abcd, wherein
abcd ->bcda -> cdab -> dabc are all words.   Can you?
Well, if you wish to stretch real words a bit, try "haha"  -> "ahah" and so on.  You know both words, the second is one of those a-hah moments.

I can find four-letter words where there are four rearrangements of the letters, each making words.
Example:  team -> meat -> mate -> tame
There are others.  This is not truly a problem. 

Word of caution... I've been hooked for years, but never got beyond what you see.
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