Subtraction combo

Udosuk, 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):
I’m proposing a trick which I think many players already knew, but I’ll formalize it here anyway. I call it “subtraction combo”. 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 column…
There it is. This is a good tip to remember if you’re solving a puzzle “offline”, without access to our site where you can use the calculator to find out which numbers could fill a cage.
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3 Comments

  1. fdkr
    Posted November 6, 2005 at 5:41 pm | Permalink

    Miyuki Misawa posts a useful table of all combinations:

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

  2. Posted November 6, 2005 at 7:46 pm | Permalink

    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.

  3. udosuk
    Posted November 7, 2005 at 3:37 pm | Permalink

    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…

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