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Simple Coloring

Suppose the candidate numbers are as pictured. Lets examine [5].

If a [5] is entered in A2, a chain of cells where [5]’s can and cannot be arises.
The yellow indicates [5]’s, the blue indicates [not 5]’s.

In the [25] cells in the middle, both cells will become [5]’s, which is impossible.

If a [1] is entered at A2, this too implies a chain, but it doesn’t end in a contradiction.

The yellow indicates [5]’s, the blue indicates [not 5]’s.

Thus, a single chain is when a problem can be solved at once, by focusing on one number. In this diagram’s case, you have to repeat [5][not 5],[5][not 5], [5][not 5], so it’s not too easy to keep track of.

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A1 | A2 | A3 | A4 | A5 | A6 | A7 | A8 | A9 |

B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 |

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 |

D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 | D9 |

E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 |

F1 | F2 | F3 | F4 | F5 | F6 | F7 | F8 | F9 |

G1 | G2 | G3 | G4 | G5 | G6 | G7 | G8 | G9 |

H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9 |

I1 | I2 | I3 | I4 | I5 | I6 | I7 | I8 | I9 |

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