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
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4
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6
7
8
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This 8×8 board rates as easy (difficulty score 652). Solving it from scratch takes 11 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, 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.
  3. Then, together, two regions have open cells only in columns G and H; 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.
  4. After that, 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.
  5. Now, 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.
  6. From there, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at C3. Region 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.
  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 G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
  10. Then, 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.
  11. Finally, place a marker at B8. Region has exactly one open cell left.

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