What changes at every step
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Step 1TIRE -> TIME
Tile 3 changes R to M; the move is sideways by letter shape. TIME has 10 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from TIRE include TORE, FIRE, WIRE, TILE.
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Step 2TIME -> TOME
Tile 2 changes I to O; the move is closer by letter shape. TOME has 14 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from TIME include LIME, DIME, TAME, TILE.
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Step 3TOME -> POME
Tile 1 changes T to P; the move is closer by letter shape. POME has 11 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from TOME include HOME, SOME, COME, DOME.
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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.