Sudoku has become quite popular and addictive for those with enough time to waste. However a good number of people give up whenever they reach a place where no more clues seem to be forthcoming or resort to trial and error methods such as using a pencil and guesswork so that it’s easy to backtrack if they make a mistake.
However, using a few simple observations, you will find a hard time coming across a Sudoku you can’t solve confidently without guessing. Before we embark let us review a few fundamentals or steps.
· Always look out for the numbers with a large frequency and try to begin by filling those ones out.
· After filling in a number always check how the new entrant affects the row, column or cube (a cluster of 9 cells) it appears in. This may be followed by trying to fill out the remaining numbers in the affected row/column/cube.
After you reach the point where it seems impossible to continue without guesswork you may try to apply the following tricks. They supply new numbers which may impossible to fill using normal rules.
1. Look for cubes/rows/columns with 3 empty slots remaining given that each has nine slots. In fig. 1 the cube highlighted in yellow has three slots remaining.
The number remaining in that cube are 1, 7 and 8. The slot marked X can only be 8 since there is 1 and 7 in column 2 already.
Another example has been supplied to reinforce the idea. In fig.2 the yellow cube has 3 remaining slots. Try and find out which number goes to the slot marked with an x. answer: 9. Numbers 5, 6 and 9 are remaining. 5 and 6 appear in column 7 leaving 9 as the number to go into slot x.
Another unrelated case in fig. 2 shows this situation in a row setting rather than cube. The 8th row has 3 empty cells remaining (to be filled with 4, 6 or 9). Numbers 6 and 9 already appear on column 7 leaving the slot marked by z to be filled with 4.
1. Another trick is to assume that some numbers can only go into certain cells without the need to know exactly which ones. In fig. 3 number 1 in the 9th row/last row ensures that number 1 in the cube highlighted with blue can only appear in either slot marked by z.
With that in mind, the slot marked x in the yellow cube can be safely filled with a 1. You either see it or you don’t. In another example as shown in fig. 4 the 2 appearing in column 1 row 8 ensures that a 2 can only appear in the slots marked z in the cube highlighted by blue.
After applying either one of these observations it might pay off to revert to the normal rules until the next dead end. Enjoy.
