QED Logic quod erat demonstrandum

An Easy 11×11 Puzzle Solved with Paired Regions in 16 Steps

11×11 · easy · 16 steps

Play this board yourself →
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This 11×11 board rates as easy (difficulty score 679). Solving it from scratch takes 16 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 row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, together, two regions have open cells only in rows 2 and 3; 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, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  4. After that, place a marker at K5. Region has exactly one open cell left. Placing here clears the rest of row 5, column K, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, 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.
  6. From there, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at J8. Region has exactly one open cell left. Placing here clears the rest of row 8, column J, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  10. Then, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region.
  11. After that, place a marker at F9. Region has exactly one open cell left. Placing here clears the rest of row 9, column F, and its region. Placing here also clears its 1 touching neighbour.
  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. Placing here also clears its 2 touching neighbours.
  13. From there, place a marker at A11. Region has exactly one open cell left. Placing here clears the rest of row 11, column A, and its region.
  14. Following that, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
  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.
  16. Finally, place a marker at G3. Region has exactly one open cell left.

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