QED Logic quod erat demonstrandum

An Easy 10×10 Puzzle Solved with Region Confinement in 11 Steps

10×10 · easy · 11 steps

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

This 10×10 board rates as easy (difficulty score 434). Solving it from scratch takes 11 logical steps, using 4 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
  2. Next, 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. Placing here also clears its 1 touching neighbour.
  3. Then, 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.
  4. After that, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, 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. Placing here also clears its 2 touching neighbours.
  6. From there, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, place a marker at H3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
  10. Then, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  11. Finally, place a marker at G10. Region has exactly one open cell left.

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