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
2
3
4
5
6
7
8
1×
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2×
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5×
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7×
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8×
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This 8×8 board rates as easy (difficulty score 667). Solving it from scratch takes 12 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, together, two regions have open cells only in columns B and A; 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, together, two regions have open cells only in columns C and D; 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.
  3. Then, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region. Placing here also clears its 1 touching neighbour.
  4. After that, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  5. Now, 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.
  6. From there, place a marker at D6. Column 4 has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  7. Following that, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
  8. First, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  9. Next, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, 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. 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. ∎