Whenever you start a consecutive sudoku, look for 1 and 9 as clues with a consecutive bar beside it. We can simply put 2 with 1 and 8 with nine since there is no other option available for these 2 digits. Also Another thing that can be borne in mind is if we have the numbers 2 and 8 in a box and they dont have a consecutive bar beside them, then the numbers 1 and 9 can never be in a cell with a consecutive bar in that box. ( this holds true if the consecutive bars are within the same box. If the consecutive bar leads to a different box then this does not apply.)

Take a look at the image below.

Another technique that is evident in this example. Look at the 8 and 2 in Box 3 and 6 respectively. In box 3, we have 8 at R1C8 and since for number 9, number 8 is the only consecutive number, 9 cannot be adjacent to 8 as there is no consecutive bar, and neither can 9 be in R2C7,R2C8 or R3C789 since all these cells have a consecutive bar, but 8 is already present in the box. Hence the only place for 9 is at R2C9.

Similarly, look at 2 in Box 6. Just like the above example, 1 cannot be in R5C789 and R6C789 since 2 is already present at R4C9. 1 also cannot be at R4C8 since there is no consecutive bar beside the 2. Hence the only place for 1 in Box 6 is R4C7.

Apart from these things always look for longer chains of consecutive numbers as they are usually the starting point of a puzzle.

Keeping this in mind let us attempt the consecutive sudoku that was displayed at this blog.

Take a look at box 2. we have a chain of 7 consecutive numbers and a chain of 2 consecutive numbers. This means that all 9 digits are part of some chain. To fulfil this criteria, the 2 digit chain has to be either 1 and 2 or 8 and 9. so the chains will be 1 and 2 and 3 to 9, or 1 to 7 and 8,9.

When we look at the 4 at R2C1 and 7 at R1C8, the chain of 3 to 9 cannot be possible. If 3 is at R3C6 then 4 has to be at R2C6 which is not possible and if 3 is at R3C4 then 7 has to be at R1C6 which is again not possible because of the 2 given digits at R1C8 and R2C1. hence the 7 digit chain is 1 to 7 and the 2 digit chain is 8 and 9. so we can safely put number 4 at R1C5. and since R3C6 is either 1 or a 7 R3C9 also has to be a 4.

Now in Box 3, the only place for the digit 8 is R2C9. If 8 were at R2C7 then R2C8 has to be 9 which doesnt allow for the 2 digit chain in Box 2. So we have 8 at R2C9 and 9 at R1C7 since there is no other place for the digit 9. and that also enables 9 at R2C4 and 8 at R1C4.

Now in R2C7 and R2C8, we can have a pair of 1,2 or 2,3 or 5,6. But 5 and 6 not possible because of the 7 digit chain in Box 2. So 5 and 6 have to be in Row 3 in box 3. Hence we have R3C7 as 6 and R3C8 as 5. Which also gives us 7 at R3C6 and the complete 7 digit chain in Box 2.

Since we have got a 3 at R2C5, R1C9 becomes a 3 and we have the chain of 1,2 at R2C7 and R2c8. since the 3 digits left at R3C1,R3C2 and R3C3 are 3,8,9 and there is a consecutive chain at R3C1 and R3C2. We can deduce that R3C3 is a 3. R3C1 is 9 and R3C2 is 8. Which also gives us R2C2 as 7 and R3C3 as 5 (naked single) for row 2. and similarly we have 1,2,6 for Row1 in box 1. so 1,2 chain is the consecutive chain and 6 comes in at R1C1.

After this the puzzle is easily solvable.

Hope this explanation was helpful and it gives you a better lead and approach to solve a consecutive sudoku.

it made for an interesting reading. but the problem is that we often do not come across the pattern as explained by you . the example that you cited is more or less known . although we do not know it as technique but whenever we come across a situation like this we know that , yes , this has to be done. but what about sudokus where we do not come across this particular pattern? to be honest , i was expecting something more for consecutive .... akash

ReplyDeleteI understand your question Akash, but then each sudoku has its own way of being solved. When we talk about a technique, it doesnt mean that all sudokus of that particular variant can be solved by it. The reason for these basic things being explained is for new comers to get an understanding as well :)

ReplyDeleteIn that context if this kind of situation is not there then it purely depends on what kind of clues are given and as I sad, always look for longer chains of consecutive digits since there will be lesser options.