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Find the minimum number of colors required to color the given graph( m - Coloring Optimization Problem)īefore starting to color the graph, one should know the minimum number of colors required to color that graph. Find out if the graph can be colored using the given set of colors. Find out all ways in which that graph can be colored using the given colors. So there are 3 different basic problems in graph coloring: If we had only 2 colors we would not be able to color it. In our above example, we had 3 colors and we were able to color it easily. Till now, what we have seen is that we were given a graph and a set of colors, to color the graph. Thus the chromatic number of this graph is 3. Similar techniques are used to solve this medium rated Sudoku puzzle.So we can see that this whole graph can be colored with a minimum of 3 colors. In addition, the 6 has only one remaining place for this row and column.įigure 9 demonstrates the different techniques that can go into finding a particular value. There are other 6s in blocks above and to the left and right. In fact, this 6 is particularly easy to spot. Usually, it would not be possible to place all the remaining numbers in sequence. On this occasion, you can place the final 6 in the bottom centre block. In the past example, you can see that the first 6 lead directly to finding the 6 in the column.Ĭontinuing along this line, it is easy to spot another 6 in the block above. Generally, it is a good idea to focus initially on the same number.
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However, the 6 can only lie in one of the 3 available squares as there is a 6 to the left of the other remaining gaps in the column. In this column, there is space for a 2, 6 and 9. Pick one and identify the numbers that are missing.
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The Sudoku has several near-complete rows and columns. The next method is very similar as it utilises the same technique, but this time for rows and columns. This method is relatively easy, provided you can identify good numbers to search for.Ĭontinuing with the same method, there is an easy 6 in the centre left block. With the row and column eliminated, there is only one square remaining for the 3 in the block. Now, both the top row and the first column of the block already contain a 3. If you look down from this block, there is a second 3 allocated to the first column in the block. You should be able to spot a 3 to the right, eliminating the possibility of another 3 in the top row. Scan for any of the numbers: 1, 2, 3, 5 or 7 that have yet to be placed in this block. Look along to the blocks to the left, right and below. Generally, it at the beginning it is wise to choose blocks that are more complete: these often lead to some easy squares to solve. Here, you can see the highlighted block has 4 out of 9 squares present. Using this knowledge, one can attempt the easiest technique: identifying a unique number to go in each block in the grid. The majority of puzzles can be solved using just one key technique.Īs you know, the numbers from 1 to 9 must be placed once in every block. Simple solving techniques The essential solving technique for all Sudoku puzzlesĪll correctly formed Sudoku puzzles are solvable using logical solving techniques.