What changes at every step
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Step 1SHUT -> SHOT
Tile 3 changes U to O; the move is closer by letter shape. SHOT has 12 legal neighbors, 3 shortest continuations, and 4 moves remaining. Other legal exits from SHUT include SHIT, SHAT, SMUT, SHUN.
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Step 2SHOT -> SHOP
Tile 4 changes T to P; the move is closer by letter shape. SHOP has 9 legal neighbors, 2 shortest continuations, and 3 moves remaining. Other legal exits from SHOT include SLOT, SOOT, SHOW, SPOT.
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Step 3SHOP -> CHOP
Tile 1 changes S to C; the move is sideways by letter shape. CHOP has 7 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from SHOP include SLOP, STOP, SHOW, SHIP.
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Step 4CHOP -> COOP
Tile 2 changes H to O; the move is closer by letter shape. COOP has 14 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from CHOP include CROP, CLOP, CHIP, CHAP.
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Step 5COOP -> POOP
Tile 1 changes C to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from COOP include LOOP, HOOP, BOOP, GOOP.