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PLEASE NOTE: for avoidance of doubt, doublers impact ALL FOUR line rules; e.g. a 6 and a doubled 3 can appear in corresponding positions in a palindrome, and a Renban line can consist of 5, doubled 3 and 7.

Normal sudoku rules apply.

"Doublers" rules apply, i.e. there is exactly one "doubler cell" in each row, column and 3x3 box, and these are the digits 1-9 once each. For the purpose of any logic relating to variant rules, the number in that cell should be considered as double the digit's face value.

Each line in this grid must satisfy the conditions of at least two of the following rulesets:
- Renban: a non-repeating set of consecutive digits in any order;
- Palindrome: a line that reads the same in both directions;
- German Whispers: consecutive digits must have a difference of at least 5;
- Equal Sums: digits on the line have an equal sum N within each box through which it passes (N.B. if a line enters the same box twice, the two segments are considered separate and must each independently sum to N).


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