QED Logic quod erat demonstrandum

A Hard 10×10 Puzzle Solved with Forced Chain in 18 Steps

10×10 · hard · 18 steps

Play this board yourself →
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This 10×10 board rates as hard (difficulty score 965). Solving it from scratch takes 18 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, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, every remaining candidate in this region touches I2 and J2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  3. Then, marking J1 would force H2, H3, H4, and 5 more cleared (together, two regions have open cells only in columns H and I), then A2, B2, C2, and 2 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then F5, F8, F9, and 4 more cleared (together, two regions have open cells only in columns F and G), and the chain continues, and then column I would be left with no open cell for its marker. So J1 can't be the marker there.
  4. After that, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, 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.
  6. From there, together, two regions have open cells only in columns J and H; 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.
  7. Following that, together, two regions have open cells only in columns F and G; 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.
  8. First, place a marker at E10. Region has exactly one open cell left. Placing here clears the rest of row 10, column E, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at A9. Region has exactly one open cell left. Placing here clears the rest of row 9, column A, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Now, 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.
  13. From there, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  14. Following that, place a marker at G5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at F2. Region has exactly one open cell left.
  16. Next, 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.
  17. Then, 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.
  18. Finally, place a marker at D4. Region has exactly one open cell left.

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