**, one of our visitors who is most active in giving hints for the puzzles we post here, has made a suggestion for a new solving technique for Killer Puzzles. He calls it “subtraction combo”. I’m posting his explanation here (slightly modified):**

*Udosuk*Iâ€™m proposing a trick which I think many players already knew, but Iâ€™ll formalize it here anyway. I call it â€œsubtraction comboâ€. For example, if you have a cage with the sum of 17, consisting of 4 cells and you narrow down the candidates to be 4 out of {2,3,4,5,6} which sum to 20. Since 20-17=3, 3 must be the odd candidate out, leaving {2,4,5,6}. Another example: a 3-cell 17-cage with possible values coming from {2,4,5,6,7}, which sum to 24. Since the 2 odd ones out must sum to 24-17=7, which can only be {2,5} here, we must have {4,6,7}. I find this technique quite useful in solving difficult killer puzzles, although it could only be applied after a cage is narrowed down to a few candidates. Hope other users will find it useful too! And if djape likes it you can describe this in details in your solving techniques columnâ€¦

## 3 Comments

Miyuki Misawa posts a useful table of all combinations:

http://www7a.biglobe.ne.jp/~sumnumberplace/31642733/

Thanks fdkr for the info. I was wondering if you have tried my calculator. I find it easier to type in what I’m looking for in the calculator and get only the needed combinations instead of looking it up in a huge table.

I know about the tables from the misawa site and djape’s calculator. But for some reason I like to do the arithmetical part in my mind instead. Normally I used a sudoku solver program to solve these (sorry not able to run djape’s perfect sudoku program on my computer), so the candidates eliminations are taken care of. With that I could normally solve djape’s killer puzzles in 30 mins to 1 hour… that includes the brain’s and IQ’s (and the supposedly “insane” a couple weeks ago). The only exception is the Sep 27 one which needed T&E… I think it would take more time if I need to refer to a table or a calculator every other move…