sudokUI › Sudoku techniques › Multi Colors
Multi Colors in sudoku
X-Chains and loops across two clusters · how it fits
For one digit X, two separate clusters of conjugate pairs are each coloured alternately in their own two colours, and a cell of one sees a cell of the other.
Why it works
Two colours that see each other cannot both be true, so X is removed from any cell outside both clusters that sees cells of both remaining colours. A colour that sees both colours of the other cluster is false: remove X from all its cells.
How to spot it
Colour two separate clusters of the same digit in four colours, then look for a unit holding a coloured cell from each cluster.
Worked example
Multi Colors on 5: two conjugate-pair clusters of 5. The purple 5s in r4c9 and r4c6 see each other (the dashed link), so they cannot both be true, and at least one of blue and gold is entirely true. The 5 in r7c2 sees the blue 5 in r8c3 and the gold 5 in r7c6, so it is false either way.
Practise it on a real puzzle. sudokUI generates a puzzle that needs Multi Colors and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs Multi Colors, the puzzle's difficulty rating grows by 200. Its class is Hard. It is needed in 1 in 890 puzzles that sudokUI generates. How the rating works.