The more difficult Sudoku puzzles can’t be solved just by using the scanning techniques of crosshatching and counting. In these more complicated puzzles, scanning will still leave you with cells where you don’t know which of two or more numbers to choose.
These puzzles will require some more detailed analysis, and most people will need to do some marking up in order to make this analysis possible – very few people can remember all of the possibilities for a large and complicated Sudoku.
Marking up involves some system of marking the remaining blank cells with the possible alternative numbers, referred to as ‘possibilities‘, ‘contingencies‘ or ‘candidates‘. If you’re solving your Sudoku on paper, don’t use a pen for marking up, because you will need to erase your markings later. Far better to use a soft pencil.
The simplest marking-up is done by using a very small script, or subscript to mark in each cell the numbers that are possible candidates for that cell. Then you erase the numbers when they are eliminated as possibilities.
The dot marking system is ideal to use on a printed Sudoku where the cells are too small to write multiple numbers in.
You place a pattern of dots on an imaginary 3 x 3 grid within the cell, to represent those numbers between 1 and 9 that are possible solutions for that cell. Erase the dots as they are eliminated from the possibilities.
The diagram on the right shows a cell marked with nine dots to represent the number 9. At the bottom right of the grid, there is a dot marking key, showing how the position of each dot represents one of the numbers between 1 and 9.
It is also possible, but less common, to use subscript or dot marking for ‘reverse marking‘, where you mark the numbers that can’t be in that cell. When there are eight numbers or dots in the cell, the missing number is the solution for that cell.
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