## Law of Leftovers

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Law of Leftovers

I created this layout today to demonstrate a technique I learned which is very usefull.
Consider this puzzle:

When you draw a line cutting off the first three columns, you have two innies R79C3 and two outies R13C4.
Because the number of innies equals the number of outies, they must share the same candidates. Other candidates which are not in commun can be eliminated.
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`..8....91........6......8..6.......9..5.2...........2.76...41.........3.9..1..47. 555566677555666777445566777444262788444222888334222888331112998333199999331111199`

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`Analysis results  Difficulty rating: 3,8 This Sudoku Jigsaw can be solved using the following logical methods: 57 x Hidden Single  2 x Direct Pointing  1 x Direct Claiming  2 x Direct Hidden Pair  9 x Cage Pointing  5 x Claiming  1 x Naked Pair  1 x Swordfish`
urhegyi

Posts: 539
Joined: 13 April 2020

### Re: Law of Leftovers

After singles the grid reduces to this situation:

The innies form a set 2369 and the outies form a set 234569.
The candidates 4/5 in set 2 are not in common and can be eliminated.
This reduces the SE rating to:
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`Analysis resultsDifficulty rating: 3,0 This Sudoku Jigsaw can be solved using the following logical methods:52 x Hidden Single 1 x Direct Pointing 1 x Direct Claiming 2 x Direct Hidden Pair 9 x Cage Pointing 5 x Claiming 1 x Naked Pair`

So no swordfish is needed anymore.
Same rule can be applied cutting off the first three rows:
The innies are now R3C12 and the outies R4C57. They must also share the same candidates. Other candidates can be removed.
Both sets have the candidates 2347 in common. 1/9 can be removed from the innies and 5/8 can be removed from the outies.
Rating is now:
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`Analysis resultsDifficulty rating: 3,0This Sudoku Jigsaw can be solved using the following logical methods: 50 x Hidden Single 1 x Direct Pointing 1 x Direct Claiming 4 x Direct Hidden Pair 6 x Cage Pointing 4 x Claiming 1 x Naked Pair`
urhegyi

Posts: 539
Joined: 13 April 2020