Sudoku Course:
Welcome to Course in Sudoku
Part 4
Hidden Candidates Reduction Method
In this part of the course we will present another method to reduce the number of candidate digits to better solve the puzzle. For this we need the candidate table as displayed by the Sudoku Instructions Program.
The method for candidate reduction that we present now is based on finding hidden candidates. Candidates are ’hidden’ if they are not alone or naked, but hidden among other candidates in a square.
If you have hidden candidates in pairs, triples or quads, you will be able to use them to perform candidate reduction. The method is based on pure logic.
If ‘hidden’ candidates are present, those digits must necessarily be in the squares where they are – they are linked to those squares. Therefore, any other candidates present in the squares with ‘hidden’ candidates can be removed from those squares.
In the squares with ‘hidden’ candidates we do not yet know where each of the digits should be placed, only that they collectively should be in those squares.
Later in the solving process the unique position of each digit will become clear. Now we will go through he method for pairs, triples and quads and give some examples. We will use the candidate table as displayed by the Sudoku Instructions Program.
Hidden Pair
If the same pair of candidate digits are ‘hidden’ among other candidates in just two squares within a group (row, column or box), then these candidate digits make up a ‘hidden’ pair. Neither of the candidate digits must be present in any other square within the group. Thus two digits are limited and therefore linked to those two squares. Therefore, other candidate digits can be removed from those two squares.
This board shows a 'hidden' pair (1 and 8, shown in blue) in column A. These candidates
are 'hidden' because other candidates are present in those squares. In column A digit
1 and 8 only occur in those 2 two squares. They are linked to those squares. Therefore
the other candidate digits, which are present in those squares, can be removed. The
candidate digits, which can be removed (3 and 9), are shown in red.
In the small picture you can see the final solution for this part of the board. In column A digit 1 should be in square A7 and digit 8 in square A9.
Hidden Triples
If the same three candidate digits are ‘hidden’ among other candidates in just three squares within a group (row, column or box), then these candidate digits make up ‘hidden’ triples. None of the candidate digits must be present in any other square within the group. Thus the three candidate digits are confined to and therefore linked to those three squares. Therefore, other candidate digits can be removed from those three squares.
This board shows 'hidden' triples (1, 2 and 7, shown in blue) in row 3. These candidates are 'hidden' because other candidates are also present in those squares. The digits 1, 2 and 7 are confined and therefore linked to those squares. Other candidate digits being present in those squares can be removed. The candidate digits, which can be removed, are shown in red.
In the small picture you can see the final solution for this part of the board. In
row 3 digit 1 should be in square A3, digit 2 in square C3 and digit 7 in square
F3.
Hidden Quads
If the same four candidate digits are ’hidden’ among other candidates in just four squares within a group (row, column or box), then these candidate digits make up ‘hidden’ quads. None of the candidate digits must be present in any other square within the group. The three digits are confined to and therefore linked to those four squares. So, other candidate digits can be removed from those four squares.
This board shows 'hidden' quads (2, 3, 4 and 6, shown in blue) in box P. These candidates
are 'hidden' because other candidates are also present in those squares. In box P
digits 2, 3, 4 and 6 are confined to and therefore linked to those squares. Other
candidate digits being present in those squares can be removed. The candidate digits,
which can be removed, are shown in red.
In the small picture you can see the final solution for this part of the board. In box P digit 3 should be in square B8, digit 6 in square C7, digit 4 in square C8 and digit 2 in square C9.
This method of finding ‘hidden’ candidates in Sudoku can be used repeatedly to reduce the number of candidate digits. Thereby the full solution of the Sudoku puzzle may be easier to obtain. This relatively simple candidate reduction method can make more difficult sudoku puzzles easier to solve.
The Sudoku Instructions Program can help you to locate ’hidden’ candidate digits as shown here.
In the beginning you can let the program find the ’hidden’ candidates and get the program to do the candidate removal.
Later when you get more experience you can also -
In the next part of the sudoku course we will present another important candidate reduction method.
Happy Sudoku Solving!
© Sudoku Instructions Programming Unit -