An Easy 10×10 Puzzle Solved with Paired Regions in 18 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 710). Solving it from scratch takes 18 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.
- First, 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.
- Next, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region. Placing here also clears its 2 touching neighbours.
- Then, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
- After that, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- Now, together, two regions have open cells only in rows 8 and 9; 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.
- From there, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
- Following that, place a marker at A10. Region has exactly one open cell left. Placing here clears the rest of row 10, column A, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
- Next, together, two regions have open cells only in columns H 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.
- Then, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
- After 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.
- Now, place a marker at E4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
- 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.
- Following that, place a marker at J3. Region has exactly one open cell left. Placing here clears the rest of row 3, column J, and its region.
- First, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region.
- Next, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
- Then, place a marker at C1. Region has exactly one open cell left.
- Finally, place a marker at H9. Region has exactly one open cell left.
The key move here was Paired regions. Once you can spot that, this board falls quickly. ∎