QED Logic quod erat demonstrandum

An Easy 11×11 Puzzle Solved with Paired Regions in 17 Steps

11×11 · easy · 17 steps

Play this board yourself →
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This 11×11 board rates as easy (difficulty score 688). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  2. Next, place a marker at B11. Region has exactly one open cell left. Placing here clears the rest of row 11, column B, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, together, two regions have open cells only in rows 9 and 10; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
  4. After that, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  5. Now, every open cell in column K belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  6. From there, place a marker at J6. Column 10 has exactly one open cell left. Placing here clears the rest of row 6, column J, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
  8. First, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  9. Next, place a marker at G4. Column 7 has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
  10. Then, every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  11. After that, place a marker at H8. Column 8 has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
  12. Now, place a marker at F10. Column 6 has exactly one open cell left. Placing here clears the rest of row 10, column F, and its region.
  13. From there, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
  14. Following that, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
  15. First, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
  16. Next, place a marker at I2. Region has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region.
  17. Finally, place a marker at K1. Region has exactly one open cell left.

The key move here was Paired regions. Once you can spot that, this board falls quickly. ∎