ave wrote:Thanks so much for the quick reply! I'm afraid I still don't see why the 39 cage can't hold a 6.
There's only one way to fill 8 cells so that the sum is 39: 1,2,3,4,5,7,8,9. There's no 6 in that list. When solving Killers or Kakuros you should probably have a look-up table with such unique combos, unless you're really good at calculating them in your head (I'm not). Mine came with a sudoku booklet I bought a long time ago, but it shouldn't be hard to create your own as well. I've memorized the combos up to 5 cells (happens automatically after a while since those combos are so common) but almost anything larger than that I would look up.
When solving killers on paper (only way I've ever done it), I use a negative dotting method to mark eliminated candidates (e.g. if candidate 1 is eliminated, I dot the corresponding spot in the cell's 3x3 space). I use the same on regular sudokus but it works especially well with killers, because at first there are many more live than dead candidates. The live candidates are represented by the non-dotted empty spaces in the cells, which might seem hard to read at first, but you get used to it. Then, when there are fewer candidates left and if you need more advanced techniques, you can mark the live candidates more explicitly (I use circles with relationship markers, but you could use regular numbers too if you find them easier to read).
If you're really stuck, SudokuWiki has a Killer solver too:
http://www.sudokuwiki.org/killersudoku.htm