Killer Sudoku

One thing that can be done with the Sudoku spreadsheet is to use it as an aid to solving Killer Sudoku problems. This is a less automated process than the usual use for solving standard Sudolu problems. However some of the features of the spreadsheet are designed for such cases.

What is a Killer Sudoku problem? Well, it's played on the same 9x9 grid, divided into 3x3 squares, into which digits 1 to 9 are put with the same constraints as in a Sudoku problem. However rather than pre-seeding the grid with some digits, the grid starts empty. Instead the grid is divided up into connected sets of cells, each of which is labelled with the sum of the digits that make it up. In some Killer Sudoku problems the addituional constraint is added that the sets also obey the Sudoku rule of no repeated digits. However in the case of the example considered here, that constraint was neither specified nor needed to solve the problem. However the solution turns out to have that property, so it may have been intended.

To consider how to use the Sudoku spreadsheet to solve a Killer Sudoku problem, an example is considered. The usual format for showing these is able to do this in black and white, but I've used colour to show the sets in this spreadsheet.

Taking the standard Sudoku spreadsheet, configure it on the Sudoku page to show Solutions and (probably) Level 3, and on the Hints page to use Right hints. As most time (all if preferring simply to us the spreadsheet for record taking) will be spent on the Hints page, on the right hand grid, this version of the spreadsheet makes those changes.

For this discussion, cells in the Sudoku spreadsheet will be labelled according to the cell numbers in the coloured spreadsheet - A1 in the top left, I9 in the bottom right and so on. Of course on the grid on which the work will take place these are cells L2 to T10. Explanation will also use rows 1 to 9, columns A to I, and 3x3 squares described as, for example, top left, centre right, and centre.

The first easy steps (in a way to solve this problem, there are of course others) are:

A spreadsheet with these settings is here. The two known cells are also filled in on the Sudoku sheet.

The next steps are the other size two sets, so for example A1+B1 being 13 means that (taking into account that 4 is already excluded from both) that these can be reduced to 5689 each. I2+I3 can be considered as a size two set summing to 14, so these also can be 5678 each. The one asymmetric set is that while G7 can be 2 (and hence G6 can be 9) G6 can't be 2, so G7 can't be 9. A sequence of eliminations is then possible:

With all the size two sets so handled, the hints are as shown here. There are still no new cells with a definite value. Can now proceed by: There are some more deductions that can be made based on these changes, but before considering them, the current state is here. This includes setting the known cells on the Sudoku sheet. Continuing: The current state is now here. Continuing: Eliminations are about to come thick and fast, so the current state is now here. Continuing: The current state is now here. Continuing: The current state is now here. Continuing: The current state is now here. Continuing: The current state is now here. Concluding: The final state is now here.

Please send any feedback to: chris@mnemosyne.demon.co.uk

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Last modified 3rd May 2009: Corrected Sudoku sheet, and added one elimination.