QED Logic quod erat demonstrandum

An Expert 10×10 Puzzle Solved with Forced Chain in 23 Steps

10×10 · expert · 23 steps

Play this board yourself →
A
B
C
D
E
F
G
H
I
J
1
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5
6
7
8
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10
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10×
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This 10×10 board rates as expert (difficulty score 1136). Solving it from scratch takes 23 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.

  1. First, 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.
  2. Next, 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.
  3. Then, together, two regions have open cells only in columns E and D; 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.
  4. 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.
  5. Now, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  6. From there, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
  7. Following that, every remaining candidate in this region touches I5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, if D3 were the marker, column E would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, that one can't be the marker: at I1 it would force G2 (the last open cell in region 1), then E5 (the last open cell in row 5), and column D would be left with no open cell for its marker.
  11. After that, marking J1 would force G2 (the last open cell in region 1), then E5 (the last open cell in row 5), and then column D would be left with no open cell for its marker. So J1 can't be the marker there.
  12. Now, place a marker at G1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
  13. From there, if I2 were the marker, it would force E5 (the last open cell in row 5), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
  14. Following that, that one can't be the marker: at J2 it would force E5 (the last open cell in row 5), and column D would be left with no open cell for its marker.
  15. First, place a marker at E2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
  16. Next, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  17. Then, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region. Placing here also clears its 1 touching neighbour.
  18. After that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  19. 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.
  20. From there, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region. Placing here also clears its 1 touching neighbour.
  21. Following that, place a marker at C10. Region has exactly one open cell left. Placing here clears the rest of row 10, column C, and its region.
  22. First, 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.
  23. Finally, place a marker at I9. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎