To complete the SUDOKU puzzle shown below left, you must place a single digit into each blank square in such a way that every row, every
column, and every box contains exactly one of each of the digits 1 to 9. The solution to this puzzle is shown below right.
SUDOKU Topics
Cell In everything that follows, cell will be taken to mean one of the 81 squares which make up the
SUDOKU puzzle.
Unit A unit is any of the following sets of 9 cells:-
Any one of the rows A to I.
Any one of the columns 1 to 9.
Any one of the boxes which are the 3x3 sets of cells delineated by the bold outlines.
The definition of the Statement of the task could now be rewritten as:-
To complete a SUDOKU puzzle you must place a single digit into each cell in such a way that every unit contains exactly one of each of the
digits 1 to 9.
Unit Intersection
A Unit Intersection is defined as the area of a SUDOKO puzzle which is common to a box and either a row or a column. The graphic
shown here demonstrates the intersection of box 7 and row H. The intersection consists of the cells H1, H2 and H3. The relationship
between the candidates in the intersection, and in the two units which intersect provides the basis for a very powerful solution
technique which will be discussed later.
Candidate
When solving any but the simplest puzzle, it is necessary to insert into each cell, a list of the numbers which could possibly
become the solution for that cell. These numbers are referred to as candidates. If you are solving the puzzle on paper you
have no option but to enter these numbers manually, which is a tiresome and error prone activity. If you are solving the puzzle
using the interactive Solve function provided by the Crossword Express program, this will be done automatically for you,
allowing you to concentrate on the more challenging task of applying the advanced solution techniques which you will encounter
shortly.
As you progress through the solving process, you will see the number of candidates gradually diminish each time you enter a new
solution number into a cell.
For those hardy individuals who refuse to use candidates, the Solve functions has an option which allows you to turn off
the automatic candidate assist mode.
Link
A link is a line joining two candidates of the same value within a unit. If there are exactly two candidates of that value within the
unit, then the link is called a Strong link, and in Crossword Express graphical displays, it will be colored dark green.
In the example shown here, the candidate is 5, and there are three Strong links. If two strong links terminate in the same unit,
then they may be connected by a link, even though there are more than two candidates of that value in the unit. Under these
circumstances, the link is referred to as a Weak link, and is colored light green. As you can see, there are two weak links in
this example.
Things start to get interesting when the links combine together to form a loop as you see here.
Links will play an important role later in several solution techniques involving Singles Chains and X-Cycles.
Difficulty Levels and Solution Techniques
When you construct a SUDOKU puzzle using Crossword Express, you can choose from 19 levels of difficulty. (More levels will be added in the
future). Each level requires the use of a new solution technique of increasing sophistication. The techniques are described in a series of
tutorial pages accessible from the index which follows. Each tutorial is accompanied by a graphic image which shows the technique in action.
These images were captured from the Request a Hint menu function of the Crossword Express SUDOKU Solve feature.
All puzzles created by Crossword Express are guaranteed to contain only single unique solution.
When you are solving a Crossword Express SUDOKU puzzle you will never need to make a guess for your next move. At every point along the
way there is guaranteed to be a valid solution technique available to allow you to make further progress. If you can't see what that
technique is, the Solve function provides a Request a Hint operation which you can call from the program menu.
If you haven't already done so, you can download a copy of Crossword Express
and install it on your Windows or iMac computer. Full instructions on how to do this are available on the download page.