duplicate numbers. However, when The Times first introduced the killer sudoku on 31 August 2005, the newspaper did not make this rule explicit. Even though the vast majority of killer sudoku puzzles followed the rule anyway, English-speaking solvers were confused about appropriate solving strategies given the ambiguity. On September 16, 2005 The Times added a new ruling that “Within each dotted-line shape, a digit CAN be repeated if the normal row, column and 3x3 box rules are not broken”. But on September 19 the rule changed to “Within each dotted-line shape, a digit CANNOT be repeated if the normal row, column and 3x3 box rules are not broken” - causing even more confusion. This revised rule stuck and the world standard is no duplicates within cages. Solving strategies Fewest possible combinations Generally the problem is best tackled starting from the extreme sums—cages with the largest or the smallest sums. This is because these have the fewest possible combinations. For example, 5 cells within the same cage totalling 34 can only be 4, 6, 7, 8, and 9. Yet, 5 cells within the same cage totaling 25 has twelve possible combinations. In the early stages of the game, the most common way to begin filling in numbers is to look at such low-sum or high-sum cages that form a 'straight line'. As the solver can infer from these that certain numbers are in a certain row or column, they can begin 'cross-hatching' across from them. The Rule of 45 A further technique can be derived from the knowledge that the numbers in all houses (rows, columns and nonets) add up to 45. By adding up the cages and single numbers in a particular house, the user can deduce the result of a single cell. If the cell calculated is within the house itself, it is referred to as an 'innie'; conversely if the cell is outside it, it is called an 'outie'. Even if this is not possible, advanced players may find it useful to derive the sum of two or three cells, then use other elimination techniques (see below for an example of this). This '45' technique can also be extended to calculate the innies or outies of N adjacent houses, as the difference between the cage-sums and N*45. Clock Arithmetic A short-cut to calculating or checking the value of a single 'innie' or 'outie' on a large number of