QED Logic quod erat demonstrandum

An Expert 8×8 Puzzle Solved with Forced Chain in 22 Steps

8×8 · expert · 22 steps

Play this board yourself →
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1
×
×
×
×
×
×
2×
×
3×
×
×
×
×
×
×
×
4×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
5
×
6×
×
×
×
×
×
×
7×
×
×
×
×
8
×
×
×
×
×
×
×
×
×
×
×

This 8×8 board rates as expert (difficulty score 1195). Solving it from scratch takes 22 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 6, 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 F5 and G5 and F7 and G7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  3. Then, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every open cell in row 1 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 open cell in row 2 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.
  6. From there, every remaining candidate in this region touches C1 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  7. Following that, if B1 were the marker, it would force D2 (the last open cell in region 3), then F3 (the last open cell in row 3), then G6 (the last open cell in region 7), and the chain continues, and column A would end up with no open cell for its marker, which can't happen. So it can't go there.
  8. First, if E1 were the marker, it would force D7 and H7 cleared (every open cell left in this region sits in row 7, so its marker has to land there), then H8 cleared (every open cell left in this region sits in row 8, so its marker has to land there), then H5 (the last open cell in region 6), and the chain continues, and region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, that one can't be the marker: at F1 it would force G6 (the last open cell in region 7), then E4 (the last open cell in region 2), and row 3 would be left with no open cell for its marker.
  10. Then, marking G1 would force F6 (the last open cell in region 7), then E4 (the last open cell in region 2), and then row 3 would be left with no open cell for its marker. So G1 can't be the marker there.
  11. After that, that one can't be the marker: at D2 it would force A1 (the last open cell in region 1), then F3 (the last open cell in row 3), then G6 (the last open cell in region 7), and the chain continues, and region 5 would be left with no open cell for its marker.
  12. Now, if D3 were the marker, it would force A1 (the last open cell in region 1), and row 2 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: at E3 it would force G4 (the last open cell in region 2), 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 G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 2 touching neighbours.
  16. Next, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
  17. Then, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  18. After that, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region. Placing here also clears its 1 touching neighbour.
  19. Now, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
  20. From there, place a marker at A1. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  21. Following that, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
  22. Finally, place a marker at B4. Region has exactly one open cell left.

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