Strategies for Number Puzzles of all kinds
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The Logic of Sudoku
  Cage Splitting

With Innies and Outies, we were looking out for single cells poking into a block or protruding outwards. We said that a block can be any combination of adjacent units (as long as they don’t overlap, like a row and a column). Sometimes, there just won’t be a single cell in one cage.

Cage Splitting example

In this example, which is the "Tough" example on the Killer Solver, we have two cage splitting examples. A side note: because the cage pattern is symetrical you should be able to find and use this strategy twice. Not all Killer puzzles are symerical, however, but it is worth looking out for.

Lets look at the yellow block - a 2 column block. We can see the straight line dividing columns 7 and 8 and jst one place where a cage pokes out. The sum of all the yellow cages - less the outie - is 75. So we now know that B8 and C8 must add up to 15 (90-75). This allows us to split the cage into two 2-cage cells, 15 and 21-15=6, the outie half. So 3,6,7,8 and 9 can be removed from C6 and C7 and 1,2,3,4 and 5 can be removed from B8 and C8.

Similarly, the 2-column blue block has a symetrically placed outie 4-cage summing to 11. The split gives us 6 as the value of the innie (F2,G2) and 5 as the value of the outie (G3,G4).

Cage Splitting doesn’t often get us whole solutions, but together with combinations (our first strategy), it can dramatically reduce the possibilities in cells. Cage Splitting can leave behind an innie or an outie elsewhere in another direction, which is also useful.

breakline

Comments...

Wednesday 3-Feb-2010

... by: steve voyce

didn't you mean c8 an d8 not b8 and c8. your highlight does not match your dotted lines. thanks steve ps i have enjoyed your sudoku solver for years. thanks.

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Article created on 13-April-2008. Views: 5705
This page was last modified on 15-January-2010, at 12:12.
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Copyright Andrew Stuart @ Scanraid Ltd, 2010