QED Logic quod erat demonstrandum

An Easy 8×8 Puzzle Solved with Paired Regions in 12 Steps

8×8 · easy · 12 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
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5
6
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8
1
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2
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4×
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6
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7×
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8
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This 8×8 board rates as easy (difficulty score 663). Solving it from scratch takes 12 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 2, 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 8, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every open cell in row 1 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.
  4. After that, together, two regions have open cells only in columns E and F; 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 G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
  8. First, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
  10. Then, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
  11. After that, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region.
  12. Finally, place a marker at A1. Region has exactly one open cell left.

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