A Medium 10×10 Puzzle Solved with Shape Squeeze in 17 Steps
Play this board yourself →A
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This 10×10 board rates as medium (difficulty score 820). Solving it from scratch takes 17 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.
- First, together, two regions have open cells only in columns I and J; 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.
- Next, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 3 touching neighbours.
- Then, 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 2 touching neighbours.
- After that, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- Now, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
- 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 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.
- First, every remaining candidate in this region touches J5 and J6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, place a marker at J7. Region has exactly one open cell left. Placing here clears the rest of row 7, column J, and its region. Placing here also clears its 1 touching neighbour.
- Then, place a marker at I5. Region has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region.
- After that, place a marker at B6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
- Now, place a marker at F8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at A1. Column 1 has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
- Following that, every remaining candidate in this region touches D10, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- 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.
- Next, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
- Finally, place a marker at D3. Region has exactly one open cell left.
The key move here was Shape squeeze. Once you can spot that, this board falls quickly. ∎