QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 14 Steps

6×6 · hard · 14 steps

Play this board yourself →
A
B
C
D
E
F
1
2
3
4
5
6
1×
×
2×
×
3×
×
×
×
×
×
4×
×
×
×
5×
×
×
×
×
×
×
×
6×
×
×
×
×
×
×
×

This 6×6 board rates as hard (difficulty score 981). Solving it from scratch takes 14 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, together, two regions have open cells only in rows 1 and 2; 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.
  2. Next, every open cell in column F 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.
  3. Then, marking A1 would force C2 (the last open cell in region 2), then B5 (the last open cell in region 4), then E3 (the last open cell in region 3), and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
  4. After that, if B1 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  5. Now, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region. Placing here also clears its 1 touching neighbour.
  6. From there, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  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 E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, place a marker at E1. Column 5 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  10. Then, every remaining candidate in this region touches B4 and B6 and C6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  11. After 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. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. From there, place a marker at F4. Region has exactly one open cell left.
  14. Finally, place a marker at B5. Region has exactly one open cell left.

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