Introduction Killer Sudoku (also known as killer su doku, sumdoku,
sum doku, addoko, or samunamupure) is derived from sudoku and kakuro. First
developed in Japan in the mids 1990s as “samunamupure”
(translated to 'sum number place'), the puzzle has been 'labeled' by the
London Times as a 'killer' puzzle due to its complexity & frustrating
complexity.
Fig. 1 Killer Sudoku Puzzle
Terminology - cell -- a single
square that contains one number in the puzzle
- row (r) -- a horizontal line of 9 cells
- column (c) -- a vertical line of 9 cells
- nonet (N) -- a 3x3 grid of cells, outlined by
borders (also referred to as a 'box' in Sudoku puzzles). The term nonet
eliminates potential ambiguity between the words “box” and “square”
- cage
-- a group of internal cells outlined by a dotted line (or by individual
colours)
- Abbreviated cell description: To describe a cage with a sum
of 23 that spans 3 cells, one could use a 'longhand' description of
“23-sum 3-cell cage”,
but for brevity I'll describe this as
“23(3)”, and the set of those 3 numbers can
be as an ordered set: [689] (i.e. in square brackets - required in exactly that
order), or as {689} (with curly brackets, to denote an unordered set in any
order)
- region (or house) --
any non-repeating set of 9 cells (can be used as a general term for 'row, cell
or nonet', and in Diagonal Killer (similar to X-Factor Sudoku) as 'long
diagonal')
Rules The objective is to fill the puzzle grid with
numbers from 1 to 9 so that the following conditions are met:
- Each row, column and nonet contains each number exactly once;
- The sum of all numbers in a cage must match the small number printed in the
cage's upper left corner;
- No number is repeated in a cage (i.e. no cage can contain more than 9 cells
but may overlap nonets);
- In Diagonal Killer Sudoku (also known as 'Killer X'), each of the long
diagonals contains each number once;
- Rule of 45: Each Sudoku region contains the
digits one through nine, adding up to 45. If X is the sum of all the cages
contained entirely in a region, then the cells not covered must sum to 45-X. By
adding up the cages and single numbers in a particular region, one can deduce
the result of a single cell. If the cell calculated is within the region itself,
it's referred to as an 'innie' (Fig. 1 - the
top-left nonet has 1 innie from 9(2)); if outside the region, it's called an 'outie'
(Fig. 1 - top-right nonet has outties from 36(6)). The 'rule of 45' can be
extended to calculate the innies or outies of N adjacent regions - as the
difference between the cage sums and N*45. Often it's useful to derive the sum
of 2 or 3 cells, then use other elimination techniques.
Hints - Since Killer Puzzles are derived from regular
Sudoku Puzzles, don't totally rely on Killer Sudoku rules alone to solve a
Killer Sudoku puzzle - use common Sudoku solution techniques as well (i.e.
Naked/Hidden Pairs, X-Wing, Colouring, Swordfish, Forcing Chains etc.) may well
help you to solve the most difficult Killer Sudoku puzzle;
Be careful not to get too hung up on analyzing every possible combination - only
resort to using combinations once you've exhausted other solution techniques.
Unfortunately, the Killer Sudoku in Fig. 1 doesn't have any of the above 'low
hanging fruit' to choose from - guess that's why it's ranked as a Diabolical
Killer Sudoku - enough to whet your appetite even further!
Looking for a World-1st combination of Sudoku and
Killer Sudoku? Try kSudoku...
