QED Logic quod erat demonstrandum

A Sharp 6×6 Puzzle Solved with Forced Chain in 18 Steps

6×6 · sharp · 18 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
×
2×
×
3×
×
×
×
×
×
×
×
×
4×
×
×
5
×
×
×
×
6×
×
×
×
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This 6×6 board rates as sharp (difficulty score 1051). Solving it from scratch takes 18 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, 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.
  3. Then, every remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, together, two regions have open cells only in columns A 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.
  5. Now, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, every remaining candidate in this region touches A4 and A5 and C5, 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 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.
  8. First, every remaining candidate in this region touches E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  12. Now, if D3 were the marker, column F would end up with no open cell for its marker, which can't happen. So it can't go there.
  13. From there, that one can't be the marker: place it at E3, and row 5 would be left with no open cell for its marker.
  14. Following that, place a marker at F3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  15. First, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region. Placing here also clears its 1 touching neighbour.
  16. Next, place a marker at E1. Region has exactly one open cell left.
  17. Then, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
  18. Finally, place a marker at C2. Region has exactly one open cell left.

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