Mental Royale
All techniques

Simple Coloring

Advanced Logic27 / 32

Paint a digit's strong links in two colors and watch one fail.

Wherever a unit holds a digit in exactly two cells, those cells form a strong link: exactly one of them is true. Chain the links together and alternate two colors — all cells of one color are true together, and the other color entirely false.

Two ways to profit: if one color appears twice in a unit, that whole color is false. And any uncolored candidate that sees both colors is false no matter which color wins.

See it in action

123456789
2
7
1
8
123456789
4
3
5
1
5
123456789
123456789
123456789
3
123456789
123456789
7
3
123456789
123456789
123456789
7
5
123456789
1
2
7
4
5
3
9
123456789
123456789
123456789
1
2
123456789
123456789
7
1
4
3
5
123456789
123456789
3
1
123456789
5
8
123456789
7
4
4
1
2
123456789
6
7
5
123456789
3
8
7
123456789
5
123456789
123456789
1
4
123456789
5
123456789
123456789
123456789
123456789
1
7
2
123456789

Step 1 of 4

The setup

Pick a digit rich in strong links (units with exactly two candidates). Color one cell, propagate along the links, and inspect: same color twice in a unit? Uncolored cells seeing both colors? Step through this real position to see it happen.

Practice

Color the strong-link chain and remove the digit from every candidate the coloring convicts.

Drill 1 of 29

Tap a cell, then the candidate digit you want to remove.