QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 16 Steps

6×6 · hard · 16 steps

Play this board yourself →
A
B
C
D
E
F
1
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3
4
5
6
1×
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2×
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3×
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4×
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This 6×6 board rates as hard (difficulty score 998). Solving it from scratch takes 16 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, 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 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.
  3. Then, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every open cell in row 5 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 remaining candidate in this region touches E2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, every remaining candidate in this region touches C5 and D5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, every remaining candidate in this region touches A4 and B4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, place a marker at E4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, place a marker at F1. Region has exactly one open cell left.
  11. After that, together, two regions have open cells only in columns D and C; 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.
  12. Now, marking B2 would immediately leave row 3 with no open cell for its marker, so it can't be the marker there.
  13. From there, place a marker at B5. Column 2 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region. Placing here also clears its 1 touching neighbour.
  14. Following that, 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.
  15. First, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  16. Finally, place a marker at A2. Region has exactly one open cell left.

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