Split Cage
More Innies-Outies
The innies - outies technique may also be used over several cells. We may split a cage into two sub cages. The relations between the various cages or sub-cages will restrict the possibilities, sometimes to a unique value or a unique possible combination.
There are several such split cages in this grid.
The innies of nonet 2 give us the sum of the two cells in blue : A = 45 - (20+22) = 45-42 = 3. They must be {12}. This also give us the sum of the other 2 cells in pink : B = 19-A = 19-3 = 16. They must be {79}. Using the abbreviated notation :
45 on N2 -> R23C4 = 3 = {12} -> R23C3 = 16 = {79}
We can now proceed to nonet 1 :
45 on N1 -> C = 45 - (18+6+16) = 5 -> D = 19-5 = 14
Then to nonet 4 :
45 on N4 -> E = 13
Notice that the two cells in R56C4 are in different cages. This is no problem. In this case the two cells belong to the same nonet (and column), so no digit may be repeated. But if they were in all different nonets, rows, columns and cages, nothing would prohibit having repeated numbers.
We now have two split cages within column 4 : A and E. We can also compute the innies of column 4 :
45 on C4 -> F1+F2 = 45 - (A+E+16) = 45 - (3+13+16) = 13
Notice that the two cells are disjoined. No problem again. Since they belong to the same column, no digit may be repeated.
BTW we could get the same result by computing innies of columns 1 to 4.
We can also compute the symetrical split cages in the right-hand side.