What changes at every step
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Step 1FOES -> DOES
Tile 1 changes F to D; the move is sideways by letter shape. DOES has 16 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from FOES include WOES, HOES, FOBS, FOGS.
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Step 2DOES -> DOER
Tile 4 changes S to R; the move is sideways by letter shape. DOER has 7 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from DOES include DOGS, DOTS, WOES, HOES.
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Step 3DOER -> DOOR
Tile 3 changes E to O; the move is closer by letter shape. DOOR has 6 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from DOER include DOUR, DEER, DYER, GOER.
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Step 4DOOR -> POOR
Tile 1 changes D to P; the move is closer by letter shape. POOR has 7 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from DOOR include MOOR, BOOR, DOOM, DOUR.
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Step 5POOR -> POOP
Tile 4 changes R to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from POOR include POOL, POOF, POUR, MOOR.