In this example the region Aa has been color coded to show the three subgroups it forms with columns a b and c. Every row and column has three sub-groups in the three regions it crosses. Whenever you allocate a square this may unlock other squares so it is worth doing the whole procedure again over the whole grid.Ī sub-group is a term used to describe three squares in a row or column that intersect a Sudoku region. You can then continue this scan through all rows then all columns in groups of three and then through all the numbers 1 through 9. The existing 2's mean there is only one place it can go - square Id. Finally in G H I there are two 2's Gg and Hc and so there is a 2 missing in row I. The same happens in rows D E F there are two 2s but both Ed and Ef are possible. In rows A B C there are 2s in Ai and Cb so there is a 2 missing in row B, however in this case there are three unallocated squares Bd Be and Bf so it can't be quickly decided in which one of these the 2 should go. Now look at the 2s in these three sets of three rows. For the last three rows there are already three 1s Gd Hb and Ig so there is no 1 remaining to be allocated. There is a 1 missing from row D and because of the 1 in Eh it can't be in Di, 1 must be assigned to Dc. Using the same logic for the following three rows D E F there is again two of them with a 1 in them: squares Eh and Ff. By elimination there is only one square a 1 can go in row B and that is in the highlighted square Bi. Because of the 1 in Ae it can not go in any other of the squares in region Ad that is Bd Be or Bf. There is no 1 in row B, it must go in one of the blank squares. Look at the top three rows where the 1s are located - they are in row A column e ( Ae) and Row C column a ( Ca) Here's an example of how it works, for more details look at our 2 out of 3 strategy page or download our puzzle solver and the free guides. First look for all the 1s then all the 2s, 3s etc. At the heart of the technique is to take groups of three rows and columns in turn, working methodically through the whole grid. It almost always finds a square or two that can be solved. It is a quick way of solving squares as it can be done in your head by scanning the puzzle grid. Some Sudoku authors refer to it as ‘slicing and slotting’. This makes extensive use of the Only Square rule. Sudoku allows squares to be solved in different ways using different strategies.Īt the incredible value of just $9 SudokuDragon offers forever usage (no subscription, no adverts), download for free trial here. Note: Whenever there are eight allocated in a group with only one remaining empty you can assign a symbol by applying either the 'only choice', 'single possibility' or 'only square' rules as all of them come down to the same thing. It doesn't matter which rule you use, as long as the square is solved. You will often find that the same square can be solved by the ‘ single possibility’ rule as well as the ‘ only square’ rule. But you can see that there is already a 3 in row I (square If) so a 3 cannot go in square Ic, the 3 must go in the other square Ac it is the only square in column c where a 3 can be allocated. In this puzzle column c (highlighted) has seven numbers allocated. This is different to the 'single possibility' rule where we looked at individual squares rather than groups. You are left with an only square within a group for a number to go in. For example if a group has seven squares allocated with only two numbers left to allocate it is quite common that an intersecting (or shared) group forces a number to go in one of the squares and not the other one. Often you will find that within a group there is only one remaining place that can take a particular number. To use this technique you choose a promising square and mentally run through each number in turn that might go in it, if you are left with only one number then that number must go in the square.įor a further in-depth guide click here Only square Sudoku rule The single possibility rule can be used to solve all the puzzle squares highlighted in green, so that makes it a very useful technique to have up your sleeve. But in row D there is already a 6 and 9 so that leaves 7 as the single possibility for square Da. Look at the purple square Da and run through possibilities: 1 2 3 4 5 and 8 that are allocated in column a leaves only 6 7 and 9 as possibilities. In this partially solved Sudoku there are quite a few readily solvable squares. So there is only one possibility for that square, and the number must go there. Because groups intersect you often find groups with more than one unallocated square but only one genuine possibility exists for one of the squares. Note: If there are eight squares solved in the group then this is just the same as the only choice rule. When you look at individual squares you often find that there is only a single possibility remaining.
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