How to solve this 8×8 logic puzzle
A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1
🐱
2
3
🐱
4
🐱
5
🐱
🐱
6
7🐱
8🐱
🐱
This 8×8 board rates as severe (difficulty score 1178). Solving it from scratch takes 30 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, 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. Placing here also clears its 2 touching neighbours.
- Next, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- Then, every remaining candidate in this region touches B3 and C3, 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 F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, if B1 were the marker, it would force C4 (the last open cell in region 3), then G3 (the last open cell in region 5), and region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, every remaining candidate in this region touches D2, 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 B4 (the last open cell in region 3), then G3 (the last open cell in region 5), and row 2 would be left with no open cell for its marker.
- First, if E1 were the marker, it would force G2 (the last open cell in region 2), then F4 (the last open cell in region 5), and region 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, that one can't be the marker: place it at F1, and region 1 would be left with no open cell for its marker.
- Then, marking G1 would force E2 (the last open cell in region 1), and then row 3 would be left with no open cell for its marker. So G1 can't be the marker there.
- After that, place a marker at D1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region. Placing here also clears its 1 touching neighbour.
- Now, if F2 were the marker, row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: place it at G2, and row 3 would be left with no open cell for its marker.
- Following that, 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.
- First, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
- Then, place a marker at C5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
- After that, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
- Finally, place a marker at A6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎