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Tue, 02 Mar 2021

What solving strategies are there for sumdoku?

Many of the solving strategies for sumdoku are the same as for normal sudoku.

For a start, you can apply the usual rules such as each number from 1 to the dimensions of the puzzle must occur once in each row and column. Therefore if there is only one place in a region where a number can go, then it must go in that location.

Similarly rules that are based on sets of cells and their possible values within the row and column regions can be applied: as the simplest example, if two cells in a row are 23,23 in terms of their pencilmark candidates, then those two values can be removed from all other cells in that region.

The main rule you will use is to work out the possible combinations within each of the cage regions, with their combination of multiplication, addition, subtraction and division. By working through the possible combinations you will be able to gradually whittle down the possible values in each cell, and in the end solve it.

Therefore keep an eye out for combinations that have low or only one possible combination. For instance if you have a "5 divide" region of two cells then you know they must be 15, 15 and you can remove those numbers from all other cells in the region. High multiplication sums are also ones that have few combinations.

Just remember that if the region is not straight - i.e. all its cells are not all in one region, then there is the possibility of repetition, therefore some candidates that you could eliminate in killer sudoku you cannot eliminate in sumdoku, and indeed sometimes those combinations that have repetition are the solution.

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