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"Easy to see"?
I don't think there is anything easy about this problem. Especially given that your example uses words much longer than 4 letters.
There may be a clever mathematical solution to this, but I don't know it.
Something like this I would probably get out some blocks and start with all the possible combinations for a 3 letter work and see how many steps it took.
Then I would do for a 4 letter word, and a five letter word. Hopefully by then a pattern would strike me.
Maybe somebody else will know off the top of their head.
for words with duplicate letters this would require a bit of work. for words without duplicate letters calculating the minimum number of moves is straight-foreword.
Yea... I was afraid that this would be a bit complicated.
Maybe I can pay for a script like this, any Idea how much I should expect to pay for a script like this?
i'll do it for $50.
Great, I'll contact you as soon as I've sold the game concept.
(I develop education games for children)