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problem with a 8 puzzle variation

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problem with a 8 puzzle variation

this is more of a challenge that was given to me by a friend who study's python to me who is trying to study it... it is a 8 puzzle variation that i can't solve (this isn't homework of sort, just a challenge that i struggle with and need guide and help)

so here it is unlike the normal 8-puzzle the challenge is using letters : a,a,b,c,d,e,f,g, (yes, there are 2 "a") and there are 3 goal variation that the can solve the puzzle, lets say : aab_cdefg , cba_adefg and gfed_cbaa and call them goalA goalB goalC

unlike a normal 1 goal 8puzzle this one must choose each move the goal he goes for goalA or goalB or goalC (in this point im trying to think how to avoid loops, going to A then switching to B then C ect... and also the double letter 'a' is a problem as i see it)

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