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Fri, 31 Mar 2017

Cracking Killer Sudoku

One of the best known sudoku variants is killer sudoku.

However, by its very name the puzzle can seem quite intimidating, as it does sound quite daunting!

The main difference between this puzzle and normal sudoku is that it is also a maths puzzle and not just a logic puzzle, as it requires addition. The dotted cages contain a number that tells you the sum of the cells in that dotted cage region, and no number can be repeated.

Cracking killer sudoku to a large extent just comes down to recognising the cages that have the least possible combinations and using this information to help whittle down the options.

Generally killer sudoku can be quite slow to get into and then solve quite quickly once you have broken the back of them; the more you solve it the more normal sudoku solving rules come into play... at the start with no numbers placed in the grid then the maths / killer sudoku element comes into it more.

When first solving these puzzles it can be useful to use a combinations table just like you might with kakuro to find which sums have the fewest combinations and then look for these in the grid. Clearly '3' and '4' from two numbers must be 2,1 and 3,1 in some order and also if you think about 17 off two numbers and 16 off two numbers then these two are good places to start for the same reason.

In addition to looking for dotted cages that have only one, or at least not very many combinations, to start whittling down the options, another rule that may not be immediately obvious but is simple to understand is the rule of 45, for the standard 9 x 9 killer sudoku puzzle.

The rationale behind this is that each region contains 1 - 9 once only. This means that the numbers in each region must always sum to 45.

This information and the interaction between the dotted cage shapes and the various regions can often help to solve a puzzle.

For instance, if you have a 3x3 box with seven dotted cage cells fully contained in the box, and the sum of those is 28, then you know that the other two cells must contain 17, which must be 9 and 8, and therefore you can write a little 9/8 in those two cells... and possibly even write in the exact values depending on the sums of the cages those two cells are in and what is already placed.

Using the rule of 45 can be very helpful in solving a killer sudoku, and many players look through each row, column and 3x3 box as the first thing they do looking for opportunities to apply the rule of 45 and make some quick and simple deductions at the start of the puzzle before then moving onto the other rules.
Date written: 16 Jan 2011

Category: killer sudoku

Keywords: killer sudoku

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