What changes at every step
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Step 1RARE -> PARE
Tile 1 changes R to P; the move is closer by letter shape. PARE has 22 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from RARE include CARE, BARE, DARE, FARE.
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Step 2PARE -> PORE
Tile 2 changes A to O; the move is closer by letter shape. PORE has 21 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from PARE include PURE, PALE, PYRE, PAGE.
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Step 3PORE -> POME
Tile 3 changes R to M; the move is sideways by letter shape. POME has 11 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from PORE include POLE, POPE, POSE, POKE.
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Step 4POME -> POMP
Tile 4 changes E to P; the move is closer by letter shape. POMP has 6 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from POME include HOME, SOME, COME, POLE.
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Step 5POMP -> POOP
Tile 3 changes M to O; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from POMP include PUMP, COMP, PIMP, ROMP.