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
B
C
D
E
F
G
H
I
1
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7
8
9
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9×
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This 9×9 board rates as easy (difficulty score 687). 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, 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, 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.
  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 columns B and C; 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.
  5. Now, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region. Placing here also clears its 1 touching neighbour.
  6. From there, 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.
  7. Following that, place a marker at B2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
  10. Then, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region. Placing here also clears its 2 touching neighbours.
  12. Now, place a marker at I3. Region has exactly one open cell left. Placing here clears the rest of row 3, column I, and its region.
  13. From there, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
  14. Finally, place a marker at G1. Region has exactly one open cell left.

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