An Expert 9×9 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
1×
×
×
×
×
×
2

×
3×
×
4×
×
×

×
5×
×
×
×
×

×
×
×
×
×
×
×
6×
×
×
×

×
×
×
×

×
×
×
×
×
×
×
×
×
×
×
×
×
×

×
×
7×
8×

×
×
×
×
9×
×
×
×
×
×
×
×
×


×
×
×
×
×
×
×
×
This 9×9 board rates as expert (difficulty score 1203). Solving it from scratch takes 24 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, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
- Next, together, two regions have open cells only in columns G and H; 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.
- Then, together, two regions have open cells only in columns B and A; 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.
- After that, every remaining candidate in this region touches D8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches H8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, every remaining candidate in this region touches A8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, that one can't be the marker: at C1 it would force H2 (the last open cell in row 2), then G7 (the last open cell in region 3), then D3 (the last open cell in row 3), and the chain continues, and region 7 would be left with no open cell for its marker.
- First, marking D1 would force H2 (the last open cell in row 2), then G7 (the last open cell in region 3), then C3 (the last open cell in row 3), and the chain continues, and then region 7 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, if E1 were the marker, it would force G7 (the last open cell in column G), then B8, A9, B9, and 1 more cleared (together, two regions have open cells only in rows 8 and 9), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, that one can't be the marker: at F1 it would force G7 (the last open cell in column G), then B8, E8, A9, and 1 more cleared (together, two regions have open cells only in rows 8 and 9), and region 7 would be left with no open cell for its marker.
- 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.
- Now, if H1 were the marker, it would force G7 (the last open cell in region 3), then B8, E8, A9, and 2 more cleared (together, two regions have open cells only in rows 8 and 9), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
- Following that, if C2 were the marker, it would force B5 (the last open cell in row 5), then A9 (the last open cell in region 7), then D7 (the last open cell in region 8), and the chain continues, and row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, 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.
- Next, every open cell in row 3 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.
- Then, place a marker at B5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
- After that, place a marker at A9. Region has exactly one open cell left. Placing here clears the rest of row 9, column A, and its region.
- Now, place a marker at F4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
- From there, place a marker at H6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
- First, place a marker at E2. Column 5 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
- Next, 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.
- Finally, place a marker at D7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎