QED Logic quod erat demonstrandum

An Easy 8×8 Puzzle Solved with Paired Regions in 11 Steps

8×8 · easy · 11 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1×
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2×
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7×
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8×
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This 8×8 board rates as easy (difficulty score 653). Solving it from scratch takes 11 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, together, two regions have open cells only in columns H and G; 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.
  2. Next, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, 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.
  4. After that, place a marker at G8. Column 7 has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region.
  5. Now, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  6. From there, every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  7. Following that, place a marker at C6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region. Placing here also clears its 2 touching neighbours.
  8. First, place a marker at D2. Region has exactly one open cell left.
  9. Next, 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.
  10. Then, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
  11. Finally, place a marker at H3. Region has exactly one open cell left.

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