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Find a path from one word to another, changing one letter at a time. You may replace, add, or delete a single letter. Each move has a cost: for replacing a letter with another, this is the square of the cyclic distance in the roman alphabet between the two letters, and for adding or deleting a letter it is the square of the distance of the letter from the start/end of the alphabet.
You may also take an arbitrary anagram, but this costs 169.
All words must be in the wordlist and have length 3 to 7. The wordlist consists of those words in the SOWPODS Scrabble list of Scrabble-valid English words whose stem (according to hunspell) has an entry in the GCIDE or WordNet dictionaries.
Each problem stays up for a day. At the end, the current winner gets a point. To become the current winner, find a path shorter (i.e. with lesser total cost) than the best found so far.
Please play without computer assistance! I'm not sure how easy it would be to bruteforce the search, since the distance formula is chosen to make A* not so effective... but I expect it would be easy to write an algorithm which outperforms a human. Please don't. If there's demand, we could have a separate competition for computer players / centaurs.