QED Logic quod erat demonstrandum

A Medium 11×11 Puzzle Solved with Shape Squeeze in 18 Steps

11×11 · medium · 18 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 800). Solving it from scratch takes 18 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, every open cell left in this region sits in column J, so its marker has to land there; that clears every other open cell in the column.
  3. Then, place a marker at K1. Region has exactly one open cell left. Placing here clears the rest of row 1, column K, and its region.
  4. After that, 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.
  5. Now, 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.
  6. From there, 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. Placing here also clears its 2 touching neighbours.
  7. Following that, 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.
  8. First, place a marker at J9. Region has exactly one open cell left. Placing here clears the rest of row 9, column J, and its region.
  9. Next, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  10. Then, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
  12. Now, place a marker at D10. Region has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at A11. Region has exactly one open cell left. Placing here clears the rest of row 11, column A, and its region.
  14. Following that, place a marker at F5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  15. First, every remaining candidate in this region touches I3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  16. Next, 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. Placing here also clears its 1 touching neighbour.
  17. Then, 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.
  18. Finally, place a marker at C3. Region has exactly one open cell left.

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