Killer Samurai Sudoku

For those who are unsure on how to solve Killer Samurai Sudoku puzzles or those who would like some tips and help to solve the puzzles faster:

Killer Samurai Rules

Killer Samurai is a modification of the basic `sudoku` and `killer` puzzles made popular in the national press. The basic rules of the puzzle are as follows:

1. Within each small 3 x 3 grid all the numbers from 1 – 9 must be used once only.
2. In each row and column of the 9 x 9 grid all of the numbers from 1 – 9 must be used once only.
3. Within each of the coloured blocks is a small number. This denotes the total value of the squares within that block. For example, if a coloured block comprising 3 squares totals 7, then the individual squares must be 1, 2 and 4, but it is down to the reader to ascertain in which order they must be placed.
4. Within each coloured block, a number may be repeated, although this is rare.
5. Each 3 x 3 grid must total 45, as must every row and column.
6. In a `killer samurai` puzzle there are 4 instances where 3 x 3 grids belong to two different 9 x 9 grids. In this situation the same rules of sudoku apply, i.e. the numbers 1 – 9 must be used once only. It stands to reason that these 4 grids can hold the key to solving the entire puzzle.

Advice as to how to solve the puzzle

1. Look for coloured blocks which contain high or low totals as these have fewer combinations of numbers and are, as such, easier to solve.
2. Look for a group of coloured blocks which protrude beyond the boundary of the 3 x 3 grid by one square only. This will allow the reader to determine at least one square of a coloured block.
3. Don`t just think of a single block totaling 45. It may sometimes be possible to ascertain a number by adding coloured blocks in 2, 3, 4 or more 3 x 3 grids totaling 90, 135, 180 etc to ascertain a single elusive number.
4. Look for intersecting coloured blocks with high or low totals. I.E. where a coloured block totaling 3 is at 90 degrees to a coloured block totaling 4, the values of the blocks should be easy to work out as there is only a choice of 3 numbers; 1, 2 and 3, but don`t forget that each row and column must contain the numbers 1 – 9 once only.
5. Look to eliminate `pairs`. If a coloured block of 2 squares totals 4, 6, 8 etc, logic tells you that the numbers contained within cannot be 2 & 2, 3 & 3 and 4 & 4 etc. thus reducing the permutations.
6. Look for coloured blocks that form `lines`. For example, if 4 coloured blocks of 2 sqaures form a line then the missing number can be calculated by deducting the total from 45.
7. Invest in a box of pencils and a good quality rubber.
8. Above all, have lots of patience and treat each puzzle as a challenge.

Number combinations.

2 square combinations

3 = 1 & 2
4 = 1 & 3
5 = 1 & 4, 2 & 3
6 = 1 & 5, 2 & 4
7 = 1 & 6, 2 & 5, 3 & 4
8 = 1 & 7, 2 & 6, 3 & 5
9 = 1 & 8, 2 & 7, 3 & 6, 4 & 5
10 = 1 & 9, 2 & 8, 3 & 7, 4 & 6
11 = 2 & 9, 3 & 8, 4 & 7, 5 & 6
12 = 3 & 9, 4 & 8, 5 & 7
13 = 4 & 9, 5 & 8, 6 & 7
14 = 5 & 9, 6 & 8
15 = 6 & 9, 7 & 8
16 = 7 & 9
17 = 8 & 9

3 square combinations

6 = 1, 2 & 3
7 = 1, 2 & 4
8 = 1, 2 & 5; 1, 3 & 4
9 = 1, 3 & 5; 1, 2 & 6; 2, 3 & 4
10 = 1, 3 & 6; 1, 2 & 7; 1, 4 & 5; 2, 3 & 5
11 = 1, 2 & 8; 1, 3 & 7; 1, 4 & 6; 2, 3 & 6; 2, 4 & 5
12 = 1, 2 & 9; 1, 3 & 8; 1, 4 & 7; 1, 5 & 6; 2, 3 & 7; 2, 4 & 6; 3, 4 & 5
13 = 1, 3 & 9; 1, 4 & 8; 1, 5 & 7; 2, 3 & 8; 2, 4 & 7; 2, 5 & 6; 3, 4 & 6
14 = 1, 4 & 9; 1, 5 & 8; 1, 6 & 7; 2, 3 & 9; 2, 4 & 8; 2, 5 & 7; 3, 4 & 7; 3, 5 & 6
15 = 1, 5 & 9; 1, 6 & 8; 2, 4 & 9; 2, 5 & 8; 2, 6 & 7; 3, 4 & 8; 3, 5 & 7; 4, 5 & 6
16 = 1, 6 & 9; 1, 7 & 8; 2, 6 & 8; 2, 5 & 9; 3, 4 & 9; 3, 5 & 8; 3, 6 & 7; 4, 5 & 7
17 = 1, 7 & 9; 2, 6 & 9; 2, 7 & 8; 3, 5 & 9; 3, 6 & 8; 4, 5 & 8; 4, 6 & 7
18 = 1, 8 & 9; 2, 7 & 9; 3, 6 & 9; 4, 5 & 9; 3, 7 & 8; 4, 6 & 8; 5, 6 & 7
19 = 2, 8 & 9; 3, 7 & 9; 4, 6 & 9; 4, 7 & 8; 5, 6 & 8
20 = 3, 8 & 9; 4, 7 & 9; 5, 6 & 9; 5, 7 & 8
21 = 4, 8 & 9; 5, 7 & 9; 6, 7 & 8
22 = 5, 8 & 9; 6, 7 & 9
23 = 6, 8 & 9 24 = 7, 8 & 9

PHEW!!!!!!

Remember that Killer Samurai Sudoku is an advanced variant of sudoku and it is highly recommended that you try to complete a normal and also killer sudoku before undertaking these more complex puzzles.

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