QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 13 Steps

6×6 · hard · 13 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 944). Solving it from scratch takes 13 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 column F, so its marker has to land there; that clears every other open cell in the column.
  2. Next, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After 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.
  5. Now, if C2 were the marker, it would force A3 (the last open cell in region 1), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  6. From there, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
  7. Following that, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  8. First, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  9. Next, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  10. Then, every remaining candidate in this region touches C4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  11. After that, 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 1 touching neighbour.
  12. Now, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
  13. Finally, place a marker at C6. Region has exactly one open cell left.

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