QED Logic quod erat demonstrandum

A Hard 8×8 Puzzle Solved with Forced Chain in 15 Steps

8×8 · hard · 15 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
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6
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8
1×
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3×
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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 hard (difficulty score 944). Solving it from scratch takes 15 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. 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, together, two regions have open cells only in rows 2 and 3; 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.
  3. Then, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, marking G1 would force H3 (the last open cell in region 4), then F5 (the last open cell in region 6), then D4 (the last open cell in region 5), and then region 3 would be left with no open cell for its marker. So G1 can't be the marker there.
  5. Now, together, two regions have open cells only in columns F 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.
  6. From there, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  7. Following that, together, two regions have open cells only in rows 4 and 5; 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.
  8. First, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at D8. Column 4 has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  10. Then, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
  11. After that, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  12. Now, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at F1. Region has exactly one open cell left.
  14. Following that, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region.
  15. Finally, place a marker at C4. Region has exactly one open cell left.

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