QED Logic quod erat demonstrandum

An Easy 8×8 Puzzle Solved with Paired Regions in 13 Steps

8×8 · easy · 13 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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3×
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4×
5×
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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 672). Solving it from scratch takes 13 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 rows 1 and 2; 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.
  2. Next, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, every open cell left in this region sits in row 4, 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 column B, so its marker has to land there; that clears every other open cell in the column.
  5. Now, every open cell in column D 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 C4. Column 3 has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region.
  8. First, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  9. Next, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, 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.
  11. After that, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  12. Now, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
  13. Finally, place a marker at H5. Region has exactly one open cell left.

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