An Expert 7×7 Puzzle Solved with Forced Chain in 20 Steps
Play this board yourself →A
B
C
D
E
F
G
1
2
3
4
5
6
7
1×

×
×
2×
×
×
×
×
×
×
×
3×

×
4×
×
×

×
5×
×
×
6

×
×
×
×
×
×
×
×
×

×

7×
×
×
×
×
×
×
×
×

×
×
×
This 7×7 board rates as expert (difficulty score 1165). Solving it from scratch takes 20 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.
- First, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
- Next, every open cell in row 7 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, every remaining candidate in this region touches F1 and G1 and F3 and G3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, that one can't be the marker: at C1 it would force D3 and D7 cleared (every open cell left in this region sits in column D, so its marker has to land there), then E5, E6 and E7 cleared (every open cell left in this region sits in column E, so its marker has to land there), then F7 and G7 cleared (together, two regions have open cells only in columns F and G), and the chain continues, and column F would be left with no open cell for its marker.
- From there, marking D1 would force C4 (the last open cell in region 6), then E3 (the last open cell in region 2), then G2 (the last open cell in region 3), and the chain continues, and then row 7 would be left with no open cell for its marker. So D1 can't be the marker there.
- Following that, if E1 were the marker, it would force G2 (the last open cell in region 3), then B3 cleared (every open cell left in this region sits in row 3, so its marker has to land there), then F7 cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and row 6 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 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.
- Next, every remaining candidate in this region touches D4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, that one can't be the marker: at B3 it would force A1 (the last open cell in region 1), then E4 (the last open cell in region 2), and region 6 would be left with no open cell for its marker.
- After that, 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.
- Now, if F2 were the marker, it would force D3 (the last open cell in region 2), and region 6 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 G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
- Following that, if D3 were the marker, region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region. Placing here also clears its 1 touching neighbour.
- 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.
- Then, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
- After that, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region. Placing here also clears its 1 touching neighbour.
- Now, place a marker at B1. Region has exactly one open cell left.
- 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. ∎