What changes at every step
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Step 1ITCH -> ETCH
Tile 1 changes I to E; the move is sideways by letter shape. ETCH has 2 legal neighbors, 1 shortest continuation, and 9 moves remaining. Other legal exits from ITCH include INCH.
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Step 2ETCH -> EACH
Tile 2 changes T to A; the move is sideways by letter shape. EACH has 2 legal neighbors, 1 shortest continuation, and 8 moves remaining. ETCH has no additional off-route exit in the sampled branch set.
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Step 3EACH -> MACH
Tile 1 changes E to M; the move is sideways by letter shape. MACH has 6 legal neighbors, 4 shortest continuations, and 7 moves remaining. EACH has no additional off-route exit in the sampled branch set.
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Step 4MACH -> MUCH
Tile 2 changes A to U; the move is sideways by letter shape. MUCH has 6 legal neighbors, 1 shortest continuation, and 6 moves remaining. Other legal exits from MACH include MATH, MASH, MACE, MECH.
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Step 5MUCH -> MUCK
Tile 4 changes H to K; the move is sideways by letter shape. MUCK has 11 legal neighbors, 4 shortest continuations, and 5 moves remaining. Other legal exits from MUCH include SUCH, MUSH, MECH, OUCH.
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Step 6MUCK -> LUCK
Tile 1 changes M to L; the move is sideways by letter shape. LUCK has 12 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from MUCK include BUCK, MOCK, HUCK, SUCK.
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Step 7LUCK -> LOCK
Tile 2 changes U to O; the move is closer by letter shape. LOCK has 18 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from LUCK include LACK, BUCK, LICK, HUCK.
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Step 8LOCK -> LOOK
Tile 3 changes C to O; the move is closer by letter shape. LOOK has 13 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from LOCK include COCK, BOCK, HOCK, ROCK.
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Step 9LOOK -> LOOP
Tile 4 changes K to P; the move is closer by letter shape. LOOP has 9 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from LOOK include BOOK, COOK, HOOK, LOOM.
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Step 10LOOP -> POOP
Tile 1 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 LOOP include COOP, HOOP, BOOP, GOOP.