Sudoku nake pairs

This article describes a particular strategy useful in solving Sudoku puzzles known as "the naked pair". The discussions will be based on the Sudoku shown in Figure 1, and which can also be downloaded here. In solving any puzzle, the first thing we can do is find all the available single candidates in the rows, columns and boxes. That is, individual cells that are the only place where particular numbers can be put. To explain this a little more, let's look at Figure 3 where we have listed all the possible numbers that can fit into each cell taking into account what already appears in the rows, columns and boxes.

Formal definition: Given a particular puzzle that has three rows where a given candidate 'C' is restricted to the same three columns, and since candidate C must be assigned once in each of these three rows no column can contain more than one of candidate C then candidate C must be assigned exactly once in each of these three columns within these three rows. Therefore, it's not possible for any other cells in these three columns to contain candidate C. This same logic applies when a puzzle that has three columns where candidate C is restricted to exactly the same three rows. Firstly, it's impossible to get very far without carefully maintaining a list of 'possible values' or candidates for each blank cell. Doing this by hand is laborious and prone to error, and often detracts from the fun of solving these puzzles. Fortunately, programs like Simple Sudoku will do this for you, while leaving you with the fun of applying logic to solve each puzzle. If you don't have a program to help - systematically analyse at each blank cell.

Naked Subsets are similar to Hidden Subsets, the only difference is that it is not about candidates being confined to cells as in Hidden Subsets , but about cells containing only a certain number of candidates. If you can find two cells, both in the same house, that have only the same two candidates left, you can eliminate that two candidates from all other cells in that house. Left example: cells r8c3 and r8c4 are both in the same house row 8 and have both only candidates 3 and 9 left. It follows immediately that on of the cells has to be 3 and the other 9 which is which is yet unknown.

The "naked single" solving technique also known as "singleton" or "lone number" is one of the simplest Sudoku solving techniques. Using this technique the candidate values of an empty cell are determined by examining the values of filled cells in the row, column and box to which the cell belongs. If the empty cell has just one single candidate value then this must be the value of the cell.