QED Logic quod erat demonstrandum

A Hard 8×8 Puzzle Solved with Forced Chain in 16 Steps

8×8 · hard · 16 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 hard (difficulty score 948). Solving it from scratch takes 16 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 7 and 8; 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 left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every open cell in column A 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.
  4. After that, place a marker at B4. Column 2 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.
  5. Now, place a marker at C1. Column 3 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  6. From there, 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.
  7. Following that, together, two regions have open cells only in columns D and E; 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.
  8. First, 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.
  9. Next, every remaining candidate in this region touches E7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  11. After that, place a marker at H3. Column 8 has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
  12. Now, that one can't be the marker: at G5 it would force F7 (the last open cell in region 8), and column E would be left with no open cell for its marker.
  13. From there, 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. Placing here also clears its 1 touching neighbour.
  14. Following 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.
  15. First, place a marker at G7. Region has exactly one open cell left.
  16. Finally, place a marker at E8. Region has exactly one open cell left.

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