Normal sudoku rules apply. Digits along grey (TEN) lines must be broken into one or more non-overlapping segments that each sum to ten. Digits may repeat within such sums if allowed by other rules. For example, 513173 is a valid fill for a length 6 line, because it can be broken into 5131 and 73, each of which sum to 10. Any set of three sequential cells along an entropic (ENT) line must contain a low digit (1-3), middle digit (4-6) and high digit (7-9). Digits may repeat on an ENT line, if allowed by other rules. Digits on a purple (REN) line form a set of non-repeating, consecutive digits in any order. Digits do not repeat along a gold (NAB) line. Additionally, no pair of digits anywhere on a gold line can be consecutive. Along green (GW) lines, adjacent digits must differ by at least 5. Digits separated by a black dot have a 1:2 ratio, meaning one is exactly double the other. Not all dots are necessarily given.