QED Logic quod erat demonstrandum

A Gentle 11×11 Puzzle Solved with Paired Regions in 20 Steps

11×11 · gentle · 20 steps

Play this board yourself →
A
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9🐱
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11×
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This 11×11 board rates as gentle (difficulty score 739). Solving it from scratch takes 20 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 K, so its marker has to land there; that clears every other open cell in the column.
  2. Next, together, two regions have open cells only in rows 10 and 11; 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.
  3. Then, place a marker at J9. Region has exactly one open cell left. Placing here clears the rest of row 9, column J, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, place a marker at K11. Region has exactly one open cell left. Placing here clears the rest of row 11, column K, and its region.
  5. Now, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  6. From there, together, two regions have open cells only in columns H and I; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
  7. Following that, together, two regions have open cells only in columns F and G; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
  8. First, together, two regions have open cells only in rows 7 and 8; 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.
  9. Next, 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.
  10. Then, together, two regions have open cells only in rows 4 and 5; 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.
  11. After that, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  12. Now, place a marker at A10. Region has exactly one open cell left. Placing here clears the rest of row 10, column A, and its region.
  13. From there, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  14. Following that, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  16. Next, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  17. Then, place a marker at G6. Region has exactly one open cell left.
  18. After that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  19. Now, place a marker at I7. Region has exactly one open cell left. Placing here clears the rest of row 7, column I, and its region.
  20. Finally, place a marker at H1. Region has exactly one open cell left.

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