QED Logic quod erat demonstrandum

An Easy 11×11 Puzzle Solved with Paired Regions in 18 Steps

11×11 · easy · 18 steps

Play this board yourself →
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This 11×11 board rates as easy (difficulty score 700). Solving it from scratch takes 18 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 J, so its marker has to land there; that clears every other open cell in the column.
  2. Next, every open cell left in this region sits in column K, so its marker has to land there; that clears every other open cell in the column.
  3. Then, together, two regions have open cells only in rows 1 and 2; 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, together, two regions have open cells only in rows 3 and 4; 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.
  5. Now, 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.
  6. From there, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  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. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 2 touching neighbours.
  9. Next, 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.
  10. Then, place a marker at I10. Region has exactly one open cell left. Placing here clears the rest of row 10, column I, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
  12. Now, place a marker at K4. Region has exactly one open cell left.
  13. From there, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region. Placing here also clears its 2 touching neighbours.
  14. Following that, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  15. First, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
  16. Next, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  17. Then, place a marker at J2. Region has exactly one open cell left.
  18. Finally, place a marker at G11. Region has exactly one open cell left.

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