Other Rainbows will be posted seperately in Other Rainbow Puzzles.
The Rainbow Killer puzzles may be X, Windoku, Semi-Symmetric or just plain killers.
Walkthroughs for the harder ones can be found on the assassin site at:
http://www.rcbroughton.co.uk/sudoku/for ... 8693#p8693
Rainbow:
The numbers are from 0-9.
There is a zero in every nonet, row and column. Zero was chosen as it increases the killer combinations, so I am sticking to it.
Each other number is missing from one and only one nonet, row and column.
It is proven that the nonet is at the crossover of the row and column.
SemiSymmetric: there are five unknown pairs of numbers.
Opposite each cell number: the opposing number is itself or its partner.
At least one cell pair is required to be self-symmetric.
From this: r5c5 = 0 zero and its partner is missing in n5, r5 and c5.
Explanation of r5c5 = 0:
Consider R5 SS so must all be anti-symmetric hence r5c5 paired with missing number R5m
Consider C5 SS so must all be anti-symmetric hence r5c5 paired with missing number C5m
Must be same missing number R5m = C5m -> r5c5 paired with missing number for N5 N5m
Four pairs must be missing from opposite nonets and one pair is r5c5 missing N5 N5m
Zero is present in every nonet so cannot be one of the four pairs, so its partner cannot be one of the four pairs, so its partner is missing from N5 = N5m so r5c5 = 0
Self-symmetric is harder to find than anti symmetric. With X as well, I have found that the only pair that is self-symmetric or split symmetry is zero and its partner (not proven).
I have been trying to find a solution where all the pairs are split symmetry - unsuccessful so far.
Note that, in my solutions I try and ensure that at least one pair is split symmetry - to avoid short-cutting, which you may chose to use in your solving path.
Rainbow Killer SS 12
Very easy, about 0.6.
