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
2
3
4
5
6
1×
×
2×
×
3×
×
×
4×
×
×
×
×
5×
×
×
×
×
×
×
×
6×
×
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This 6×6 board rates as hard (difficulty score 1008). Solving it from scratch takes 16 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, 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 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.
  3. Then, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  4. After that, 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.
  5. Now, every remaining candidate in this region touches F3, 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 B2 and B3 and D3, 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 B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, if E1 were the marker, region 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, 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. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at B6. Column 2 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  12. Now, 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.
  13. From there, 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.
  14. Following that, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
  15. First, place a marker at A4. Region has exactly one open cell left.
  16. Finally, place a marker at E5. Region has exactly one open cell left.

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