Let's play the first Sudoku game at third level hardness
This is the first game play at Sudoku third level. For absolute beginners this is quite a high level, but just like any other human activity area, if you are experienced it would seem easy to you. In this first game play at the third level we didn't find the game difficult though we have used advanced technique of Digit Subset Analysis extensively.
Notice in the game below that number of cells filled up is significantly less than the games at level 2 or 1 we played till now. The number of filled up cells is only 27 with empty cells to be filled up 54. Earlier we were solving games with 47 to 51 empty cell boards.
But number of empty cells is not the only criterion of hardness, there are others such as bunching up of digits in one area. We are just indicating that this game might really be harder than previous games.
Hard or not, having reached a fairly good comfort level, we don't get mentally stalled or unduly cowed down by the hardness of any problem and deal with the problem as naturally as possible. The more formal stages of problem solving such as problem analysis, problem modeling etc. get automatically included in this approach. So we will play this game in a flow using the techniques developed through playing the past games as they come.
We will now go for game play without any more delay.
The Sudoku third level game 1
First valid cells, R1C2 5, scan R2, R3, C1 -- R9C4 2, scan R7, R8,C5 -- R4C2 2, scan R5, R6, C3 -- R9C2 8, scan R7, R8, C3 -- R3C5 4, DSA [1,3,4,5] in C5.
Here we will stop and see the DSA in a bit more details. In C5 five cells are occupied and so it has the status of a favorable zone. To evaluate its potential we give a broad horizontal scan across the rows intersecting with the empty cells of C5. This is a skill we have developed for identifying a zone, column, row or a 9-cell square for DSA. With just a look we find the row R3 cutting across C3 at one of its empty cell locations is quite well populated. So we form mentally a set of the possible digits in the empty cells as [1,5,3,4] and check that set for occurrence of its digits in the intersecting favorable row R3. And sure enough, we find to our joy that out of [1,5,3,4] three digits [1,5,3] already appear in the row R3 leaving only the single digit 4 to happily occupy the cell R3C5.
Immediately after one successful DSA result, the length of DSA gets reduced, in this case to [1,5,3], and as you can guess, this reduction in DSA length makes the zone more favorable. That's why more often than not we follow one long DSA to its end when we get a first success out of it.
One important point to note here, we use two favorable zone concept: the first is the more occupied zone (row, column or 9-cell square) in which the DSA is formed and the second is the intersecting more occupied row column or 9-cell square.
We will follow the same DSA for more successes here, R1C5 1, DSA [1, 3, 5] in C5 -- R9C5 3, DSA [3,5] in C5 -- R7C5 5 -- R7C3 7, DSA [3,4,6,7] in R7, a new DSA -- R9C3 1, DSA [1,6,7] in R9 -- R9C9 6, DSA [6,7] in R9 -- R9C8 7 -- R4C3 5, DSA [5,9] in C3 -- R2C3 9 -- R4C8 6, scan R5,R6,C9 -- R3C9 9, long DSA [1,3,4,5,9] in C9.
A few words about long DSAs here are pertinent. A five digit long DSA is quite long. But we are so accustomed with analyzing potential DSA success that we resort to such a long DSA analysis without any hesitation. and that too we do it fast. The ability depends on the skill in evaluating the potential of a DSA at two levels simultaneously. With practice and well-defined goals you should be able to develop the skill easily. Remember, one success with a long DSA may break the problem apart.
Taking up the game again, this long DSA didn't result in further successes with same DSA, but it reduced the emptiness and played its part towards the solution well.
A few steps more, R3C8 2, DSA [2,6,7] in R3 -- R1C8 3, DSA [1,3,4,6,7] in top right 9-cell square. Again a long DSA but this time in a 9-cell square.This is quite a breakthrough and we will see a lot of DSA cancel and easy successes in the following steps. We will see in the following steps that we have already achieved the main breakthroughs.
The result is shown in the following game board. We will go over to next stage then.
This stage starts with, R7C8 4, DSA cancel -- R8C7 3, DSA cancel -- R6C7 4, DSA cancel -- R4C9 3, DSA cancel -- R2C8 1, DSA [1,5,8,9] in C8 -- R8C8 5, DSA cancel -- R8C9 1, DSA cancel -- R2C9 4, DSA [4,5] in C9 -- R5C9 5 -- R4C6 7, DSA cancel -- R4C4 4 -- R8C6 6, DSA cancel -- R8C4 7, DSA cancel -- R1C6 2, DSA cancel -- R2C6 8, DSA cancel -- R2C4 6 -- R2C2 3, DSA cancel -- R2C1 2 -- R7C2 6, DSA [3,6] in R7 -- R3C2 7, DSA cancel -- R1C1 6 -- R1C7 7 -- R3C7 6 -- R7C1 3 -- R6C1 9 DSA [4,7,9] in C1 -- R8C1 4, DSA [4,7] in C1 -- R5C1 7 -- R5C2 4, scan R6 -- R6C2 1 -- R8C2 9 -- R5C8 9, scan R6 -- R6C8 8 -- R5C6 1, DSA [3,1] in C6 -- R6C6 3 -- R6C4 5 -- R5C4 8. Game solved.
In hindsight, now we understand, the back of the problem was broken during the previous stage in a few special DSA successes, as in this stage we did mostly easy DSA cancels and soft scans towards final solution.
Overall this game didn't pose any difficulty.
An important note on writing Digit Subsets or DSs in empty cells
Notice that usually we haven't written DSs in empty cells longer than 2 digits. The reason lies in effectiveness of 2 digit long DSs in empty cells. As soon as you are able to form a two digit DS in an empty cell, you know the cell to be just one step away from becoming a valid cell by DSA cancel. Furthermore, you never know when a pair of a two digit DS will apppear in the same zone, form a cycle and reduce the complexity of the game considerably. Forming longer than 2 digit cycle is not easy, it is error prone and we avoid it.
In general writing longer than two digit DSs in empty cells is wasteful and we avoid it. But we never let go an opportunity to write a two digit DS in an empty cell.
The final result is shown below.
A special note for you
We haven't tried to optimize. So we feel that this more complex game is solvable by following an easier path.
You should try to reach one of the simpler solutions.
This time again we will leave you with two game to solve. In our next episode we will go through solutions of these two games and will offer two more games for you to solve.
Two games for you to solve
We leave you here with two new games to solve.
Second game at Third level of hardness
Third game at third level of hardness