QED Logic quod erat demonstrandum

A Hard 8×8 Puzzle Solved with Forced Chain in 17 Steps

8×8 · hard · 17 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
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3
4
5
6
7
8
1×
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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 hard (difficulty score 979). Solving it from scratch takes 17 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, 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.
  4. After that, 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.
  5. Now, every open cell in row 2 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.
  6. From there, every remaining candidate in this region touches E1 and F1 and E3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  7. Following that, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, that one can't be the marker: at C1 it would force E4 (the last open cell in region 2), then F2 (the last open cell in region 3), then H6 (the last open cell in region 6), and row 3 would be left with no open cell for its marker.
  9. Next, every open cell in column C 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.
  10. Then, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  11. After that, together, two regions have open cells only in rows 5 and 6; 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.
  12. Now, place a marker at F2. Column 6 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
  13. From there, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
  14. Following that, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
  15. First, place a marker at C3. Region has exactly one open cell left.
  16. Next, 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.
  17. Finally, place a marker at B6. Region has exactly one open cell left.

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