What changes at every step
Letter positions: 4-2-3-4-1. Letter changes: E>T, A>O, S>O, T>P, C>P.
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Step 1CASE -> CAST
Tile 4 changes E to T; the move is sideways by letter shape. CAST has 15 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from CASE include CAME, CASH, BASE, CAGE.
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Step 2CAST -> COST
Tile 2 changes A to O; the move is closer by letter shape. COST has 10 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from CAST include CASH, CYST, LAST, PAST.
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Step 3COST -> COOT
Tile 3 changes S to O; the move is closer by letter shape. COOT has 17 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from COST include COAT, COLT, HOST, LOST.
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Step 4COOT -> COOP
Tile 4 changes T to P; the move is closer by letter shape. COOP has 14 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from COOT include COOK, COOL, COOS, HOOT.
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Step 5COOP -> POOP
Tile 1 changes C to P; the move is closer by letter shape. POOP has 12 legal neighbors, target reached, and 0 moves remaining. Other legal exits from COOP include HOOP, LOOP, GOOP, CHOP.