### ... by: Jigancio

Hi

I'm sorry, but alas! this 'only' is not a solution, it gets stuck again a little later "run out of valid strategies"

Yes, of course, as I posted, g5+g6+g7=19, and the same g5+g6 plus f6 sum up also 19 (box).

Thus, necesarily g7=f6, that's the trick, and we can remove 4 from f6 and 9 from g7, what now leads to the solution (j7=9 and so on).

No doubt, you have improved the solver, but in my opinion it still lacks a routinary and effective way of detecting which squares are the same value in order to inmediately eliminate single candidates.

Sincerely yours

J. Ignacio Fernández

Andrew Stuart writes:

I understood your trick but dont have a way of generalising it yet. I agree my enhancement doesn’t solve this puzzle but it's very useful over many puzzles. Still working on your strategy. I'll post more when I get there!

Thanks

### ... by: PeteTy

todays killer took me 40min was very challenging

the thing that broke it for me was the c8-c9 triple innie 11

http://www.sudokuwiki.org/killersudoku.htm?bd=122111122113322212122113311332122212313313332213212113212212443231331211331131233,250900260000001300000007001000002000000600200009000000190000001700000015001518001209000000150000210008040014000000000000080000000920130011150700000000000000001000

so i loaded it in the solver

r78 single innie

n9 single innie

row 1-4 has dual outie 16 for a 7 9 pair

the solver spotted all those

box1 has a dual outie of 2

i noticed that before the singles but,

the solver never did spot it .. solver found the 1 to the south with some magic multiple cage interactions and exotic hard cage combinations

after it found the 1 to the east in the 7(2) cage,

it took several solve steps before it discovered the 6

I dont consider that particular combination to be a tough one ...

did notice the solver has:

Innies (2 to 4 cells)

doesnt have:

outies (2 to 4 cells)

a little thought will confirm outies dont have the cage convention (no doubles) while innies do

---------------------------------------------------

order of the steps the way i solve vs the solver

ill do cage splitting innies outies cage combinations way before hidden triples quads

way before y wings, colouring or pointing pairs

i really think the tough strategy on the killers shouldnt start before the normal sudoku tough strategy

perhaps move the blue ones (killer specific) to lower numbers

### ... by: PeteTy

there are a few caveats involved with multiple innies and outies

just look at the lack of the killer cage convention

a fun example (last above) gives N1+N2

an innie 36 or 90-(22+15+17)

a 9 cell pseudo-cage

it cant have 6 or 9 because they are required in the 22(3) and 17(3) cage

possibles

Digit Combinations - Can't Have Digits 69 Must Have Digits1234578

9 cell cage

36: 112345578* 122344578 123334578

Digits 1234578 Combinations 3

just look at the lack of the killer cage convention

n2 above sums to 14(4) outie

n8 has a 32(5) outie

both of these happen to have no repeated digits

r5 has an outie 14(3) very easy to spot

r1+r2+r3+r4+r5 has an outie 6(1) a single

which leaves an outie 8(2) for r5 to r9

its confined to row 4 and must have no repeated digits so 44 is not in the possibles

when i start getting stumped with a killer i may see n1 with a 2 cell outie

one goes east the other south

outie 4

2 cell cage

4: 13 22

Digits 123 Combinations 2

outie 10

Digit Combinations -

2 cell cage

10: 19 28 37 46 55

Digits 123456789 Combinations 5

outie 18

2 cell cage

18: 99

Digits 9

### ... by: DavidC

Thanks for a great site. In the pseudo-cage section of Innies and Outies, you say "D7 and E7 form a pseudo-cage of size 2 and a 'clue' of 5. That could be 1/4 or 2/5." There is a typo : it could be 1/4 or 2/3. Regards, David.

### ... by: MK

@akansha

So the concept of Innies and Outies is this: since any given row, column, or box of nine squares contains the digits 1-9, it must add up to 45 (1+2+3+...+9=45). Therefore, if you have a given set of cells that overlap said row/column/box, plus an extra square (an outie) or minus a square (an innie), you can calculate the value of that square.

Example: a row made up of the followings four cells (the numbers are the sums, underscores is a blank square:

[12 _] [12_] [12_][7_] [_]

[_ _ _][ _ _ _][_ _][_]

The last underscore is part of a two-square cell overlapping the row below. In this case, it's an Innie, because all the other cells are contained in this one row. So you add the sums of the cells: 12+12+12+7=43. You know that the total sum of the row must equal 45. So, 45-43=2 means that the square on the end by itself must be a 2.

It would work the same way for an Outie, except that the total sum of the cells would be greater than 45 and the empty square would be on a different row. (Example: total sum is 48. 48-45=3, so the 3 goes in the Outie square.)

Then you just expand this for multiple rows/columns/boxes. If the sum of one row is 45, then the sum of two rows is 90, the sum of three rows is 135, and so on.

I hope that this helps to clarify. I know that it's hard to visualize when I don't have proper pictures like above.

### ... by: akansha

Could not understand the concept of Innies and outies.

Can you be more elaborated/descriptive?

With example.

### ... by: Kaylea

I didn't know where to find this info then kboaom it was here.