What changes at every step
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Step 1SUES -> SUMS
Tile 3 changes E to M; the move is sideways by letter shape. SUMS has 14 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from SUES include SEES, DUES, CUES, SUED.
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Step 2SUMS -> SUMP
Tile 4 changes S to P; the move is closer by letter shape. SUMP has 10 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from SUMS include SUMO, BUMS, HUMS, RUMS.
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Step 3SUMP -> PUMP
Tile 1 changes S to P; the move is closer by letter shape. PUMP has 11 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from SUMP include JUMP, DUMP, BUMP, LUMP.
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Step 4PUMP -> POMP
Tile 2 changes U to O; the move is closer by letter shape. POMP has 6 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from PUMP include PIMP, JUMP, DUMP, BUMP.
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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 COMP, PIMP, ROMP, POME.