Some time ago now, the Cracking the Cryptic Sudoku community experienced something between a fascination and an obsession with "159 Sudoku", which spawned a whole new subgenre of so-called "indexing Sudoku". One of the first things that happened was the combination of 159 Sudoku with other common variant rules. Previously, I had only seen 159 Sudoku appearing in its pure form, but the combination with other variants, particularly mathematical ones, made some interesting properties of the indexing columns apparent. Here is my take on the combination with X-Sums, one of my favourite variants.
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Rules
Place a number from 1 to 9 into each empty cell so that every row, column, and bold-outlined region contains every number exactly once. Additionally, the following variant rules apply:
159 - If X is the number placed in row N, column (1/5/9), then (1/5/9 respectively) must appear in row N, column X. For example, if row 3, column 5 is a 7, then row 3, column 7 is a 5.
X-Sums - A clue outside the grid indicates the sum of the first X numbers placed in the corresponding direction, where X is the first of those numbers.
Difficulty: 7/10
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