Toroidal Killer Sudoku 10×10 puzzle

So far all of the “pure Sudoku logic” in my puzzles posted here has been pretty gentle.  Well I decided that it was time to change that, but of course I wasn’t about to do that with a common garden puzzle!  So I’ve applied some harder logic to this 10×10 Killer Sudoku with toroidal cages.

Because this is a 10×10 puzzle I’ve kept the Killer Sudoku part very easy – there are plenty of single cages (with apologies to those who dislike these!) and although the maths goes a tiny bit higher the actual ‘Killer reasoning’ is straightforward.  But the Sudoku reasoning itself is definitely tougher, in places.

So here are the rules:

• Place 1 to 10 into each row, column and bold-lined 5×2 cage
• Place numbers so that they add up to the total at the top-left of each dashed-line cage
• Numbers may not repeat within a dashed-line cage
• Some cages wrap around the edges of the puzzle – they continue in the same row/column on the opposite side of the puzzle (so a cage leaving off the right of row 3 continues on the left edge of row 3, and vice-versa)

In summary, then, there are a few relatively unusual things here: the 1-10 Killer sums and 1-10 Sudoku; the toroidal cages; and the fact that this Killer requires tough Sudoku logic and so plays more like a 1-10 regular Sudoku than a 1-10 Killer… once you get going, that is!

Good luck!