From Sudopedia, the free Sudoku reference guide
Split cage
From Sudopedia
In Killer Sudoku, a cage can sometimes be split into two via the application of the 45 rule. The resultant cages are known as split cages. At the same time, the constraints of the original cage still apply, so we get three times the solving power of the original cage.
Example
We use the following as an example. Pay attention to the 10[4] cage that straddles across both nonets.
Recall that the 45 rule states that the digits in any row, column or nonet must sum up to exactly 45.
Now we focus on the left nonet, and consider the 22[3], 10[4], 9[2] and 8[2] cages. Since 22 + 10 + 9 + 8 = 49 = 45 + 4, we find that the two outies the left nonet must sum up to 4, hence we can split the 10[4] cage into two along the nonet boundary, with the right cage being 4[2] and the left cage being 6[2]. The result is shown below.
The newly produced 4[2] cage must only contain the {1,3} combination. Although a typical 6[2] cage may contain {1,5} or {2,4}, but since the 4[2] cage is a Naked Pair, the 6[2] cage cannot contain {1,5} due to the Killer Convention applied to the original 10[4] cage. Hence, the 6[2] cage gets only the {2,4} combination.
The useless looking 10[4] cage now becomes two very productive Naked Pairs.
