GridWits
Extreme tier Technique 17 of 18 Used by Smart Hint

Every Path Agrees

List every way an island could still fill out its size — then cross off any that would break the water around it, like trapping a 2×2 pool. A cell in all the survivors is land; a cell in none of them is sea. Often the checks leave just one way, which settles the whole pocket at once.

How it works

  1. 1The 4 has one cell so far and five open cells to grow into — list the ways it could pick its three remaining cells. Eight different shapes fit the space.
  2. 2Now check what each shape does to the water around it. A finished island is walled in sea on every side — and for seven of the eight shapes, that wall (plus the leftover cells, which would all have to become sea) traps a 2×2 pool of water or cuts the sea in two. Those shapes were never really possible.
  3. 3Only one shape survives every check: the three cells straight along the bottom. All three are land, and the pocket is settled in a single realization.
  4. 4The same idea as checking a Sudoku cell's candidates against every remaining valid arrangement of a region — applied to an island's shape, with the water's own rules doing the eliminating.
1 1 1 1 4 1
  • Island (land)
  • Sea
  • Cells that establish the pattern
  • Where the conclusion lands
Next in the ladder Proof by Contradiction →

When nothing else advances the puzzle, try one cell's two possible states and follow the consequences a few steps ahead. If one choice breaks a rule, the other is forced.