QED Logic quod erat demonstrandum

A Gentle 11×11 Puzzle Solved with Paired Regions in 13 Steps

11×11 · gentle · 13 steps

Play this board yourself →
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This 11×11 board rates as gentle (difficulty score 651). Solving it from scratch takes 13 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 A, so its marker has to land there; that clears every other open cell in the column.
  2. Next, 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 3 touching neighbours.
  3. Then, 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.
  4. After that, 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.
  5. Now, place a marker at K8. Region has exactly one open cell left. Placing here clears the rest of row 8, column K, and its region.
  6. From there, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 2 touching neighbours.
  7. 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. Placing here also clears its 2 touching neighbours.
  8. First, place a marker at J4. Region has exactly one open cell left. Placing here clears the rest of row 4, column J, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, 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.
  11. After that, place a marker at F11. Region has exactly one open cell left. Placing here clears the rest of row 11, column F, and its region.
  12. Now, place a marker at D10. Region has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region.
  13. Finally, place a marker at C2. Region has exactly one open cell left.

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