QED Logic quod erat demonstrandum

An Easy 9×9 Puzzle Solved with Paired Regions in 14 Steps

9×9 · easy · 14 steps

Play this board yourself →
A
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G
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I
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This 9×9 board rates as easy (difficulty score 679). Solving it from scratch takes 14 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, 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.
  2. Next, together, two regions have open cells only in columns A and B; 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.
  3. Then, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  5. Now, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  6. From there, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
  9. Next, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  10. Then, 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.
  11. After that, place a marker at I6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region.
  12. Now, place a marker at C9. Row 9 has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region. Placing here also clears its 1 touching neighbour.
  13. 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.
  14. Finally, place a marker at G8. Region has exactly one open cell left.

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