What changes at every step
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Step 1GAGS -> BAGS
Tile 1 changes G to B; the move is sideways by letter shape. BAGS has 20 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from GAGS include TAGS, GAYS, GAPS, GALS.
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Step 2BAGS -> BOGS
Tile 2 changes A to O; the move is closer by letter shape. BOGS has 19 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from BAGS include BASS, BUGS, BATS, BAYS.
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Step 3BOGS -> BOOS
Tile 3 changes G to O; the move is closer by letter shape. BOOS has 21 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from BOGS include BOYS, BOSS, BOTS, BOWS.
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Step 4BOOS -> BOOP
Tile 4 changes S 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 BOOS include BOOK, BOOT, BOOB, BOOM.
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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.