What changes at every step
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Step 1HUSH -> LUSH
Tile 1 changes H to L; the move is sideways by letter shape. LUSH has 9 legal neighbors, 1 shortest continuation, and 5 moves remaining. Other legal exits from HUSH include PUSH, HUSK, BUSH, RUSH.
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Step 2LUSH -> LUST
Tile 4 changes H to T; the move is sideways by letter shape. LUST has 12 legal neighbors, 1 shortest continuation, and 4 moves remaining. Other legal exits from LUSH include PUSH, LASH, BUSH, RUSH.
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Step 3LUST -> LOST
Tile 2 changes U to O; the move is closer by letter shape. LOST has 13 legal neighbors, 1 shortest continuation, and 3 moves remaining. Other legal exits from LUST include LIST, LAST, LEST, JUST.
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Step 4LOST -> LOOT
Tile 3 changes S to O; the move is closer by letter shape. LOOT has 16 legal neighbors, 1 shortest continuation, and 2 moves remaining. Other legal exits from LOST include COST, HOST, LOFT, LOUT.
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Step 5LOOT -> LOOP
Tile 4 changes T 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 LOOT include LOOK, BOOT, LOOM, LOON.
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Step 6LOOP -> 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.