What changes at every step
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Step 1RAIL -> FAIL
Tile 1 changes R to F; the move is sideways by letter shape. FAIL has 14 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from RAIL include TAIL, PAIL, ROIL, MAIL.
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Step 2FAIL -> FOIL
Tile 2 changes A to O; the move is closer by letter shape. FOIL has 10 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from FAIL include FALL, TAIL, PAIL, MAIL.
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Step 3FOIL -> FOOL
Tile 3 changes I to O; the move is closer by letter shape. FOOL has 10 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from FOIL include FOUL, COIL, FOWL, TOIL.
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Step 4FOOL -> POOL
Tile 1 changes F to P; the move is closer by letter shape. POOL has 8 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from FOOL include TOOL, COOL, WOOL, FOOD.
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Step 5POOL -> POOP
Tile 4 changes L to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from POOL include POOR, POOF, TOOL, COOL.