What changes at every step
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Step 1BRAG -> BRAT
Tile 4 changes G to T; the move is sideways by letter shape. BRAT has 11 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from BRAG include BRAS, BRIG, FRAG, CRAG.
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Step 2BRAT -> BOAT
Tile 2 changes R to O; the move is closer by letter shape. BOAT has 11 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from BRAT include BEAT, BRAS, BRUT, PRAT.
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Step 3BOAT -> BOOT
Tile 3 changes A to O; the move is closer by letter shape. BOOT has 20 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from BOAT include COAT, BOLT, BOUT, BOAR.
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Step 4BOOT -> BOOP
Tile 4 changes T to P; the move is closer by letter shape. BOOP has 12 legal neighbors, 1 shortest continuation, and 1 move remaining. Other legal exits from BOOT include BOOK, BOOB, BOOM, BOON.
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Step 5BOOP -> POOP
Tile 1 changes B to P; the move is closer by letter shape. POOP has 11 legal neighbors, target reached, and 0 moves remaining. Other legal exits from BOOP include LOOP, COOP, HOOP, GOOP.