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## Cross Sums Sudoku

So the question is: Does giving totals for all outer 3 cells (across and/or down) in selected 9×9 squares give the ability to solve a sudoku puzzle with a reduced collection of starting numbers? Because the interior (to the left of the 4th column and above the 4th row) has no space to specify their sums, I’ve chosen normal starting numbers instead.

The book by Xin-She Yang, Ph.D., called Cryptic Kakuro and Cross Sums Sudoku offers cross sums of all the 9×9 squares by creating wider detachments between them. There are no starting numbers as a result.

This puzzle also differs from traditional Kakuro Puzzles in that the entire 9×9 grid is used. In Kakuro, only a subset of the grid is used. See my cartoon on Kakuro last May 27, 2007.

Although I tried to offer all possible sums (combinations) of 3 unique single digits 1 through 9, there are too many to list. Trust in symmetry to help furnish the rest of them, if needed.

In other news, the 3rd Annual World Championship Sudoku Competition has just provided some downloadable materials for study and sample variations that (we and) the contestants may work on. Note that in the individual competition, Sudoku variants score double the points of Classical Sudoku puzzles where the expected solving time is the same.

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## Sudoku To Kakuro

I’ve been doing Cross-Sum puzzles for many years, but now that it’s called Kakuro (abbreviation of Japanese kasan kurosu: addition cross), it seems somehow new. Certainly the Puzzle book publishers think so. Where there was previously only a section in a crossword puzzle book there is now entire puzzle books devoted to Kakuro.

In solving these kinds of puzzles it may be useful as a solving aid to know about minimum and maximum values for the length of each clue number and a way of dealing with missing and required values in partial sums. One such way is to map missing values to 0 and required values to 1, to get a bit-wise string of bits for which bit-wise logical operations can be performed: and, or, exclusive or, not.