A Hard 10×10 Puzzle Solved with Forced Chain in 24 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 hard (difficulty score 1098). Solving it from scratch takes 24 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 row 6, so its marker has to land there; that clears every other open cell in the row.
- Next, together, two regions have open cells only in columns A and B; 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, 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.
- After 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.
- Now, 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.
- From there, every remaining candidate in this region touches A7 and B7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Following that, place a marker at B6. Column 2 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.
- First, 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. Placing here also clears its 1 touching neighbour.
- Next, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- Then, 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.
- After that, every open cell left in this region sits in column J, so its marker has to land there; that clears every other open cell in the column.
- Now, 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.
- From there, together, two regions have open cells only in rows 4 and 5; 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.
- Following that, every remaining candidate in this region touches I4 and I5, 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 E8 and F8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, every remaining candidate in this region touches I8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, if H4 were the marker, it would force J5 (the last open cell in region 5), then I7 (the last open cell in region 9), then F9 (the last open cell in region 6), and column E would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, marking J4 would force H5 (the last open cell in region 4), then I7 (the last open cell in region 9), then F9 (the last open cell in region 6), and then column E would be left with no open cell for its marker. So J4 can't be the marker there.
- Now, place a marker at J5. Region has exactly one open cell left. Placing here clears the rest of row 5, column J, and its region.
- From there, 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.
- Following that, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
- First, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at I10. Region has exactly one open cell left. Placing here clears the rest of row 10, column I, and its region.
- Finally, place a marker at A9. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎