Very similar to naked pairs but here we have 3 possible numbers for 3 cells. When we look at the image below, in box 5 and column 6, we have 1,2,3 as possible numbers for the 3 cells, R4C6,R5C6,R6C6, which have been circled. The buddy cell to all thes e3 cells is highlighted in yellow which is R2C6.
Hence 3 is eliminated from R2C6 and we have only the number 5 as a possibility for R2C6.
If any two cells in a row, Column or 3x3 box has the same 2 possible candidates then those two numbers can be eliminited from the buddy cells of both those cells. The example below will make it clear.
In Row1, R1C2 has the possibilities of 5,9 and also R1C8 has the possibility of 5 and 9 again. Hence irrespective of where the 5 and 9 come in these 2 cells, they cannot occur in any cel which is a buddy to both these cells. Cell R1C9 is a buddy to R1C2 and also to R1C8 hence neither 5 nor 9 can be in R1C9. Similarly, if we look at Box 2, R2C5 and R3C5 both have possibilities of 3 and 4 so irrespective of that neither number can be in R3C6 which is a buddy to R3C5 and R2C5.
Any cell that has only one number as a possibility is known as a Naked Single. Look at the circled cell R4C4 in the image given below.
The numbers 2,3,8,9 are eliminated as they already occur in the row 4. The numbers 4,5,6 are also eliminated since they occur in Column 4 and the number 7 is eliminated as it already occurs in Box 5. Hence the only possibility for the circled cell R4C4 is the number 1. This is known as the Naked Single Technique.
If any digit can occur in only one cell in any Row, Column or 3x3 Box, among all possibilities for that cell, then it becomes a hidden single for that cell. The images below will give a better explanation.
The first image shows all the pencil marks (possible numbers for any given cell). We have four possibilities for the cell at R6C6, viz. 2569.
Now when we look at the second image, I have yellowed out all the cells in Box 5, where the number 5 cannot occur due to the 5 at R2C4 and R4C3.
so that allows for number 5 to be in R6C6 only. The reason it is called hidden single is because in the first image there were other possibilities too for the cell R6C6 and the number 5 was hidden amongst them. Though the terminology is just FYI, I thought I will share it with you.
In a given Sudoku, every cell in the grid has 20 buddy cells. The buddy cells are highlighted in green in the given image below. In the example the number 1 is in cell R1C1 (R1C1 being Row 1 and Column 1) All the green cells are buddy cells to R1C1 and cannot contain the number which is already there in R1C1.
XYZ-Wing is similar to XY Wing, except that the cell which contained the possibility of XY also has a third possibility of Z. Take a look at the image. Cells which are buddy to ALL 3 marked cells are highlighted in yellow.
Since Z is common in all 3 marked cells and has to be in one of these 3 marked cells, it is eliminated from all the buddy cells to these 3 marked cells. Lets take a look at the example below.
Cells, R4C2, R4C4 and R6C4 form an XYZ-Wing with R4C being the cell with possiblity XYZ. Here the value of Z is 2. Cell R4C6 is highlighted since it is buddy to all the 3 marked cells. (same row as R4C2 and R4C4, and same box as R6C4. Since the number 2 has to be in one of the three marked cells, it is eliminated from R4C6.
XY Wing is an elimination technique by using a combination of 3 numbers. Lets say the 3 numbers are X,Y and Z. Now take a look at image below.
There are 3 cells each with a combination possibility of X,Y,Z. R1C5 has a possibility of X or Y. R2C4 has possibility XZ and R1C7 has possibility YZ. note that the cell containing XY is a buddy cell to both XZ (Same Box )and YZ (Same Row). Cells which are buddy to both YZ and XZ are highlighted in yellow.
Now if R1C5 if value is X, the number Z has to be in R2C4. If R1C5 is Y then Z ha to be in R1C7. So either ways Z has to be in either R1C7 or R2C4. Hence the number Z cannot be in the highlighted yellow cells. Now let us take a look at an actual example.
The cells R2C2, R2C4 and R3C1 form an XY Wing, where R2C2 is the cell with possibility XY. Irrespective of what the value of R2C2 is, 6 will always be in either R2C4 or R3C1. The highlighted yellow cells are buddy cells to both R2C4 and R3C1 hence 6 can be eliminated from these cells.
Coincidentally, if we look at R3C4,R3C5 and R3C6 they form Naked Triplets