QED Logic quod erat demonstrandum

A Medium 11×11 Puzzle Solved with Shape Squeeze in 22 Steps

11×11 · medium · 22 steps

Play this board yourself →
A
B
C
D
E
F
G
H
I
J
K
1
2
3
4
5
6
7
8
9
10
11
1×
×
×
×
×
×
×
2×
×
3×
×
4×
×
×
×
×
×
5
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
6×
×
×
×
×
7×
×
×
×
×
×
×
×
×
×
×
8×
×
×
×
×
9×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
10×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
11×
×
×
×
×
×
×
×
×
×

This 11×11 board rates as medium (difficulty score 860). Solving it from scratch takes 22 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze. 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 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.
  3. Then, every open cell left in this region sits in row 11, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every remaining candidate in this region touches I2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, 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.
  6. From there, place a marker at J1. Region has exactly one open cell left. Placing here clears the rest of row 1, column J, and its region.
  7. Following that, every open cell left in this region sits in column K, so its marker has to land there; that clears every other open cell in the column.
  8. First, 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.
  9. Next, 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.
  10. Then, 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.
  11. After that, place a marker at I4. Region has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region.
  12. Now, together, two regions have open cells only in rows 3 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.
  13. From there, together, two regions have open cells only in columns F and E; 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.
  14. Following that, every remaining candidate in this region touches E5 and F5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  15. First, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  16. Next, place a marker at E6. Region has exactly one open cell left. Placing here also clears its 2 touching neighbours.
  17. Then, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  18. After that, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 2 touching neighbours.
  19. Now, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
  20. From there, place a marker at K10. Region has exactly one open cell left. Placing here clears the rest of row 10, column K, and its region.
  21. Following that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  22. Finally, place a marker at C11. Region has exactly one open cell left.

The key move here was Shape squeeze. Once you can spot that, this board falls quickly.