An Expert 8×8 Puzzle Solved with Forced Chain in 23 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 1237). Solving it from scratch takes 23 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.
- 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.
- Next, 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.
- Then, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, marking A1 would force D4, E4, F4, and 2 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then D6, E6, F6, and 2 more cleared (every open cell left in this region sits in row 6, so its marker has to land there), then B7, B8, C3, and 3 more cleared (together, two regions have open cells only in columns B and C), and then region 8 would be left with no open cell for its marker. So A1 can't be the marker there.
- Now, if B1 were the marker, it would force A7, A8, C3, and 3 more cleared (together, two regions have open cells only in columns A and C), and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: at C1 it would force D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), then A7, A8, B7, and 1 more cleared (together, two regions have open cells only in columns A and B), and region 8 would be left with no open cell for its marker.
- Following 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.
- First, marking D1 would force C4, C6, C7, and 1 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then A7, A8, B7, and 1 more cleared (together, two regions have open cells only in columns A and B), and then region 8 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, that one can't be the marker: place it at F1, and row 2 would be left with no open cell for its marker.
- Then, marking G1 would force D2 (the last open cell in region 1), then C5 (the last open cell in region 4), then A6 (the last open cell in region 7), and then region 3 would be left with no open cell for its marker. So G1 can't be the marker there.
- After that, if H1 were the marker, it would force D2 (the last open cell in region 1), then C5 (the last open cell in region 4), then A6 (the last open cell in region 7), and region 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, place a marker at E1. Row 1 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.
- From there, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region. Placing here also clears its 2 touching neighbours.
- Following that, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
- First, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
- 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.
- Then, every open cell in column H 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.
- After that, every open cell in column D 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.
- Now, every remaining candidate in this region touches C6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
- Finally, place a marker at H7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎