## Let's play the fifth Sudoku game at third level of hardness

This is the fifth game play session at Sudoku third level of hardness. For many this may be quite a high level, but just like any other human activity area, if you are experienced it would seem easy to you. In this fifth game play at the third level while playing the game we needed to use two or three digit long cycles through frequent use of DSA. Once we could form such cycles, things started getting easier.

As is the custom, we will still use row-column scan, but Digit Subset Analysis or DSA will be the main technique along with Cycles. To know what a **Cycle** or **DSA** is you may refer to our * first* and

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**second game play sessions at level 2**Let us play the game.

### The Sudoku 5th game play at third level of hardness

First valid cells, R4C1 6, scan C3,R5 -- R8C2 6, scan C1,C3,R9 -- R6C5 6, scan R4,R5,C6 -- R7C4 6, scan C5,C6,R8 6 over -- R4C3 7, scan R5,R6 -- R8C1 7, scan C3,R9 -- R5C1 9, scan C2,R6 -- R7C3 9, scan R9 -- R9C2 8, DSA [2,8] in R9 -- R9C3 2 -- R5C5 3, scan R4,R6 -- Cycle (1,4) in C9 -- Cycle (2,8) in C9 -- R7C9 7, DSA [7,9] in C9 -- R2C9 9 -- R3C7 7, scan R1,C8,C9 -- R2C2 7, scan R1,R3,C1 -- R3C6 9, scan C4,C5,R1,R2.

The results achieved till now are shown below. Next valid cell will be our breakthrough or turning point.

R4C7 cannot be 4 as it will generate three (1,8) cells in the middle 9 cell square which is not possible. So, R4C7 8. This is our breakthrough point.

If you examine this situation closely, you will appreciate that 4 in row R4 can appear in only two cells R4C4 or R4C5 in the middle 9 cell square. This is kind of hidden cycle and this disallows the presence of digit 4 in R4C7 making 8 as the valid digit in R4C7.

Our next valid digits will come easy, Cycle (1,4) in middle 9 cell square, R6C6 8 -- R6C9 2, DS cancel -- R8C9 8, DS cancel -- R6C7 5, DS cancel -- Cycle (1,4) in R5, R5C2 5 -- R6C3 1 -- R3C2 1 -- R1C3 3, DS cancel -- R3C3 5 -- R1C4 1, scan R2,R3 -- R4C4 4, DS cancel -- R4C5 1 -- Cycle (2,4) in R7, R7C8 5, DSA [5,8] in R7 -- R7C5 8 -- R2C4 8, scan R3,C5,C6 -- R1C1 8, scan R2,R3 -- R2C5 5, Cycle (2,3,4) in R2 -- R8C4 5, scan C5,C6 -- R3C4 3.

The results are shown in the board below. We will go over to the next and final stage.

The first valid cells at this stage are, R2C8 3, Cycle (2,4) in R2 -- R9C7 3, scan C8,C9 -- R8C6 3, scan R7,R9,C5 -- R8C5 2, DSA [2,4] in C5 -- R3C5 4 -- R2C6 2 -- R2C1 4, DS cancel -- R3C1 2 -- R7C6 4, DS cancel.

And the last few cells, R9C6 1 -- R9C9 4, DS cancel -- R5C9 1, DS cancel -- R5C8 4 -- R7C7 2, DS cancel -- R8C8 1 -- R1C7 4 DS cancel -- R1C8 2. Game solved. End.

The final result is shown below.

As usual we leave you here with a new game to solve.

Enjoy.

#### Sixth game at Third level of hardness

### Other Sudoku game plays at third level hardness

**How to play hard third level Sudoku, game play 9**

**Sudoku Third level game play 8**

**Sudoku Third level game play 7**

**Sudoku Third level game play 6**

**Sudoku Third level game play 4**

**Sudoku Third level game play 3**