An Expert 7×7 Puzzle Solved with Forced Chain in 21 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 1222). Solving it from scratch takes 21 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 column C, so its marker has to land there; that clears every other open cell in the column.
- Next, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
- 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.
- After that, every remaining candidate in this region touches E1 and E2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches B5 and B6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- From there, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
- Following that, marking A1 would force D2 (the last open cell in region 2), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
- First, marking G1 would force D2 (the last open cell in region 2), then E4 cleared (every remaining candidate in this region touches E4), then B4 (the last open cell in region 4), and the chain continues, and then region 6 would be left with no open cell for its marker. So G1 can't be the marker there.
- Next, if F2 were the marker, it would force D1 (the last open cell in region 2), then E5 (the last open cell in region 5), then B4 (the last open cell in region 4), and row 3 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 G2 it would force D1 (the last open cell in region 2), then A3 (the last open cell in row 3), then E4 (the last open cell in region 4), and region 5 would be left with no open cell for its marker.
- After that, if A3 were the marker, it would force F1 (the last open cell in region 3), then D2 (the last open cell in region 2), then E4 (the last open cell in region 4), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, marking F3 would immediately leave region 3 with no open cell for its marker, so it can't be the marker there.
- From there, if E4 were the marker, it would force F1 (the last open cell in region 3), then D2 (the last open cell in region 2), then G3 (the last open cell in region 5), 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.
- Following that, place a marker at B4. Region 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.
- First, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
- Next, that one can't be the marker: at F1 it would force D2 (the last open cell in region 2), then A7 (the last open cell in region 1), then G5 (the last open cell in region 6), and row 3 would be left with no open cell for its marker.
- Then, 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.
- After that, place a marker at D1. Region has exactly one open cell left.
- Now, 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.
- From there, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
- Finally, place a marker at A2. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎