Sudoku Solver

Extreme

Simple Coloring

Use two colors to trace a single candidate across the grid. If a cell sees both colors, it can be eliminated.

Simple Coloring (or Single's Chain) is an easy-to-understand strategy because it uses no complex math—just two colors, like Blue and Green.

It works by tracking a single number (e.g., "Where can the 2s go?").

Interactive Example

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

Click "Apply Logic" to see the strategy in action.

Real Example Explanation

In the example above, we are tracking the number 2.

  1. The Chain:
    • We look for "Strong Links" (rows, columns, or boxes where 2 appears exactly twice).
    • We pick a starting pair and color one Blue and the other Green.
    • If a Blue cell is connected to another pair, the other end becomes Green (and vice versa).
    • This creates a "Daisy Chain" of alternating colors across the grid.
  2. The Logic:
    • Since every link is an "either/or" choice, the entire Blue set is tied together, and the entire Green set is tied together.
    • Scenario A: All Blue cells are 2 (and Greens are not).
    • Scenario B: All Green cells are 2 (and Blues are not).
    • Result: The real 2s are either all the Blues or all the Greens.
  3. The Elimination (Type 2):
    • Look at cell R3C2.
    • It sees a Blue candidate (at R3C9).
    • It also sees a Green candidate (at R6C2).
    • Since one of those colors must be real, it is impossible for R3C2 to be a 2. (If it were 2, it would break both the Blue chain and the Green chain).
    • Therefore, we remove 2 from R3C2.

How to Spot It

  1. Pick a Number: Focus on one candidate (like 2).
  2. Find Pairs: Look for houses (row/col/box) where that number appears exactly twice.
  3. Start Coloring: Mental or pencil. Mark the first one A (Blue) and the second B (Green).
  4. Extend: If a Blue cell connects to another pair, mark the new partner Green.
  5. Check for Conflict:
    • Type 1 (Chain Broken): If two cells of the same color see each other, that color is false. (All cells of that color are removed).
    • Type 2 (Intersection): If an uncolored cell sees both colors, remove the candidate from that cell.

Comparison

  • Remote Pairs: Uses a chain of pairs (two numbers).
  • Simple Coloring: Uses a chain of single numbers.
  • X-Wing: A very short Simple Coloring chain (length 4).

Related Strategies