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 Killer Cage Combination Example From sudokuwiki.org, the puzzle solver's site
 This example shows the kind of logic involved in using cage combinations in Killer Sudoku. There are many leaps of logic to be found in this type of puzzle, and this should also explain in more detail some of the results from the Killer Sudoku Solver. In this instance the solver returnsKILLER STEP (Hard) on D3: shape of length 3 with clue of 15+ can only be 1/2/3/4/5/6/8/9, removing 7The question is - why does it eliminate the 7 in D3 and not D1?Hovering over the 15 on the small board it lists the combinations. There are quite a few in this cage:1/5/91/6/82/4/92/5/82/6/73/4/83/5/74/5/6 Killer Cage Combo Example
Now...

1/5/9 <-- no 7 used at all
1/6/8 <-- no 7 used at all
2/4/9 <-- no 7 used at all
2/5/8 <-- no 7 used at all
2/6/7
3/4/8 <-- no 7 used at all
3/5/7
4/5/6 <-- no 7 used at all

So if 7 is used (either D1 or D3) the combos are

3/5/7
2/6/7

But there is no 3 in the cage, so we are left with

2/6/7

Try and fit that in the cage - it can only go one way with the candidates that remain:

7/6/2 fits in D1,D2,D3
But there is no 2 and 6 in D1 and D2 if D3 is a 7

Voila...if - and its still and IF...7 is used the solution will be {7,6,2}, so the solver will remove 7 from D3.

Of course we don't know if 7 is actually used in the combo so that's as far as we can take it at this stage.

 Article created on 21-April-2011. Views: 2853This page was last modified on 21-July-2011, at 12:12.All text is copyright and for personal use only but may be reproduced with the permission of the author. Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2011