An Expert 10×10 Puzzle Solved with Forced Chain in 26 Steps
Play this board yourself →A
B
C
D
E
F
G
H
I
J
1
2
3
4
5
6
7
8
9
10
1×
×
×
×
2

×
×
×
×
3×
×
×

×
×
×
×
×
×
×
4×
×
×
×
×
×

×
×
×
×
×
×

×
5×
×
×
×
×
×
×
×
×
×

×
×
×
×
6

×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
7×

×
×
×
×
×
×
×
×
×
×
×
8

×
9

×
×
×
10×
×
×
×
×
×
×
×
×
×
×
×
×

×
This 10×10 board rates as expert (difficulty score 1224). Solving it from scratch takes 26 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 9 and 10; 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, place a marker at J8. Region has exactly one open cell left. Placing here clears the rest of row 8, column J, and its region. Placing here also clears its 1 touching neighbour.
- Then, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
- After that, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
- Now, 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.
- From there, every open cell left in this region sits in row 10, so its marker has to land there; that clears every other open cell in the row.
- Following that, every remaining candidate in this region touches E4 and G4 and E5 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- First, every remaining candidate in this region touches A5 and B5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, marking A1 would force B6 (the last open cell in region 6), and then column C would be left with no open cell for its marker. So A1 can't be the marker there.
- Then, if B1 were the marker, it would force A6 (the last open cell in region 6), then E9 (the last open cell in region 9), then C5 (the last open cell in column C), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, that one can't be the marker: at C1 it would force E9 (the last open cell in column E), then H3 and I3 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A3, A4 and B4 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and row 10 would be left with no open cell for its marker.
- Now, marking D1 would force C5 (the last open cell in column C), then F4 (the last open cell in region 5), and then region 3 would be left with no open cell for its marker. So D1 can't be the marker there.
- From there, 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.
- Following that, 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.
- First, marking G1 would force H7 (the last open cell in region 7), then I10 (the last open cell in region 10), and then region 3 would be left with no open cell for its marker. So G1 can't be the marker there.
- Next, if H1 were the marker, it would force G7 (the last open cell in region 7), then I10 (the last open cell in region 10), and region 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 I1 it would force G10 and H10 cleared (together, two regions have open cells only in columns G and H), and row 10 would be left with no open cell for its marker.
- After that, place a marker at E1. Region 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.
- Now, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region.
- From there, 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.
- Following that, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
- First, place a marker at G3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column G, 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 D4. Region has exactly one open cell left.
- After that, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
- Finally, place a marker at I10. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎