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
2
3
4
5
6
7
8
9
1×
×
×
2×
×
×
×
3×
×
×
×
4×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
5
×
×
×
×
×
×
×
×
×
×
6×
×
×
×
7×
×
×
×
8
×
×
×
×
×
×
×
×
×
×
×
×
×
9
×
×
×
×
×

This 9×9 board rates as easy (difficulty score 673). Solving it from scratch takes 14 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line 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 9, 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 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.
  3. Then, 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.
  4. After that, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  5. Now, every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  6. From there, place a marker at A8. Column 1 has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region.
  7. Following that, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region.
  9. Next, place a marker at C3. Column 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  11. After that, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
  12. Now, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
  13. From there, 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.
  14. Finally, place a marker at D9. Region has exactly one open cell left.

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