## Learn how to solve expert Sudoku level 5 game 18 quickly

The very hard expert Sudoku level 5 game 18 is solved step by step by advanced Sudoku techniques of Single digit lock, parallel scan and double digit scan.

Sections are,

**Expert Sudoku level 5 game 18****Solving Expert Sudoku level 5 game 18 by advanced Sudoku techniques and strategy****Expert Sudoku Strategy and techniques for quick solution**.**What is a Cycle of twins or triplets and how to use it in solving an expert Sudoku puzzle****How to find a naked single in a valid cell by Possible Digit Subset Analysis (DSA).**.**Single digit lock and how to use it in solving an expert Sudoku puzzle**-
**Expert Sudoku technique of double digit scan.** **Expert Sudoku technique of parallel digit scan for a single digit on a row or a column.**

*You may move directly to any of the above sections by clicking its link and return to previous position by clicking on browser back button.*

**While going through the solution** you may click on say **Cycle** whenever it appears, to know how to form and use a Cycle and then return to the previous position to continue through the solution.

*In the same way, for the other techniques also you may jump to details of a technique and after refreshing your concept return to the point from where you jumped.*

### Expert Sudoku level 5 game 18

The following is the Sudoku puzzle that should engage your mind for some time. The Rs are the row labels, Cs are the column labels and this we define as the stage 1 marked on top left corner.

We'll **first solve the Sudoku hard** using **strategies and techniques for solving Sudoku hard puzzles.**

The strategy and techniques for quickly solving Sudoku hard are explained with examples in the sections after the solution.

You may decide to go through the solution directly and take a look at the specific strategy or technique when you feel like.

The Sudoku hard techniques with internal links to the concept sections appear in the solution. You may just click on any such link, say for example * Cycle,* go through the concept and return by clicking on browser back button.

Or, you may decide first to go through the concepts and then go through the solution. To jump to the Strategy and techniques concept sections click **here.**

Following is the **solution of the puzzle explained step by step in details.**

*Please spend your time fruitfully on the game trying to solve it before going through the solutions.*

### Solving Expert Sudoku level 5 game 18 by advanced Sudoku techniques and strategy: Stage 1: Breakthroughs by Digit subset analysis, Sigle digit lock, Double digit scan

Let us solve our Expert level 5 Sudoku hard puzzle now.

We'll show the puzzle again for ease of understanding.

*To follow the details accurately, you should better have the game actually with you written on paper, or better still**—**created in a spreadsheet.*

**R3C1 1** row column scan R1, R2, C3. **Effective single digit lock on 2** in R2C7,

**R2C8** by row column scan for 2 in R3, C9.

An **unexpected Cycle (5,6) created in R1C1, R2C1: double digit scan for [5,6] in C2** and **aided by a single digit lock on 6 in R7C3, R8C3 with 5 also in C3.**

The Cycle reduces digit subset in C1 to [3,4,8] -- **R5C1 3 by reduction** of [4,8] in R5 -- **Cycle (4,8)** in C1.

**Unexpected valid digit R5C7 1 by DSA**: DS [1,2,5,7,9] reduced by [2,5,7,9] with [2,7] in middle right major square and [5,9] in C7.

More breakthrough s next stage.

Status Shown.

### Solving Expert Sudoku level 5 game 18 Stage 2: Breakthroughs by parallel digit scan, Cycles, Digit subset analysis

**R6C2 1** by scan for 1 in C3, R5. **Cycle (1,9)** in R7C6, R8C6 by **double digit scan for for [1,9] in R9, C5** -- R4C4 1 row column scan for 1 in R6, C5, C6.

Next **breakthrough by parallel digit scan for 9 on column C4** -- **R6C4 9** by 9 in R9 and 9 in top middle major square.

**R7C5 5** by scan for 5 in R9.

**Cycle (2,4,6)** in R9C4, R9C5, R9C6 by leftover digits in R9. **R4C6 5** scan for 5 in R6 and C5. **Cycle (3,4)** in R2C6, R3C6 in C6 by reduction of 2 because of 2 in single digit lock in R2. **R9C6 2** reduction, **R9C4 6, R9C5 4**.

**R6C6 8** by scan 8 in C5. **R3C4 8** reduction, **R2C4 5, R1C4 2, R1C5 6**.

**R1C1 5, R2C1 6** reduction. **R6C1 4, R4C1 8** reduction. **DS [3,6,7] reduces by 7 in middle right major square to form Cycle (3,6) in R6** -- **R6C5** 7 reduction.

**R4C5 3** scan 3 in R5 -- **R5C5 2** residual. **R4C3 2** scan 2 in R5.

DS [4,9] in R4C7 reduces by 9 in C7 -- **R4C7 4** -- **R4C9 9** residual.

**R5C8 5** scan 5 in R4, R6. **R8C9 5** scan 5 in R7, R9, C7, C8. **R4C9 1** scan for 1 in R9, C7, C8.

**R8C7 6** DS reduction from [2,4,6,9] by [4,9] in C7 and 2 in R8.

**Cycle (3,4)** by DS reduction of [1,9] in bottom left major square from DS [3,4,1,9].

**R8C8 9** by reduction -- **R8C6 1, R7C6 9. R7C2 8** reduction, **R7C3 6**.

Status shown.

### Solving Expert Sudoku level 5 game 18 Stage 3: Breakthroughs by parallel digit scan, double digit scan, Digit subset analysis, Cycles

**R1C3 8** by **parallel digit scan for 8 on R1 by 8 in C2, C9.**

**Cycle (2,8)** by **double digit scan for [2,8] in R3, C9.** **Cycle (3,4,7)** in C9 in R1C9, R2C9, R9C9 -- **R3C9 6** leftover.

**Cycle (3,4)** in R3C6, R3C8 -- **R3C3 7** leftover. **R5C3 9** reduction -- **R5C2 7** reduction.

**R2C2 9** scan for 9 in R1, C3. **R2C9 7**.

Status shown.

### Solving Expert Sudoku level 5 game 18 final stage 4: All easy pickings

With 7 in R3C9, **R9C9 3** reduction, **R9C8 8, R9C7 7.**

**R1C9 4** residual, **R1C2 3** residual, **R2C3 4** residual, **R8C3 3** residual, **R8C2 4** residual.

**R2C6 3** reduction, **R3C6 4** residual, **R3C8 3** residual. **R6C8 6** reduction, **R6C7 3** residual.

With 8 in R9C8, **R2C7 8** scan, **R2C8 2** residual, **R7C7 2** residual, **R7C8 4** residual.

Final solution shown.

Check for the validity of the solution if you need.

### Expert Sudoku Strategy and techniques for quick solution

As a strategy * we always try first—the row-column scan to find the valid cell *at any stage, because that is the

**most basic and easiest of all techniques.**

When easy breaks by row-column scan becomes hard to come by, the next technique is used.

**Next easy to use technique used is**—identification of single valid digit for a cell by **Digit Subset Analysis** or **DSA** in short. This technique is explained in a following concept section.

And wherever possible, **Cycles** are formed that in any situation are a treasure to have and Cycles play a key role in quick solution. Concept and use of Cycles are explained in a following section.

You may wait for Cycles to form automatically in a column or row.

But a **proactive approach of forming a Cycle by DS analysis** speeds up the solution process considerably. This is what we call forced creation of Cycles.

The **last resort of filling EACH EMPTY CELL with valid digit subsets** is to be taken when it is absolutely necessary. Only with all empty cells filled with valid digit subsets, the possible breakthrough points in a hard puzzle can be discovered.

Strategically for faster solution, it is better to delay this time consuming task as much as possible.

In **hybrid strategy,** a few of the cells of interest are filled with DS of shorter length and analyzed for a breakthrough such as forming a Cycle or a single digit lock.

One of the most powerful patterns that we have used for highly positive result each time is the **lock of a single digit in a row or column inside a 9 cell square** so that the digit is eliminated from all other DSs in the locked row or column outside the 9 cell square.

The necessity of use of this **digit lock technique** indicates in a way the hardness of the puzzle. This technique is also explained in a following section.

A **basic part of overall strategy** is,

Whether we search for a

breakthrough of a bottleneckor avalid cell identification, our focus usually is on thepromising zones,the zones (row, column and 9 cell square combined) that contain larger number of filled digits including Cycles.

The main strategy should always be to adopt the easier and faster technique and path to the solution by looking for key patterns all the time. Digit lock, Cycles, Valid cell by DSA are some of the key patterns.

Focus when solving a hard Sudoku puzzle should be on using the technique that would produce best results fastest. Easy to say, not so easy to do**—comes with practice.**

### What is a Cycle of twins or triplets and how to use it in solving an expert Sudoku puzzle

#### Form of a Cycle:

In a Cycle, the digits involved are locked within the few cells forming the cycle. The locked digits can't appear in any other cell in the corresponding zone outside the few cells forming the cycle.

For example, if a 3 digit cycle (4,7,8) in column C2 is formed with a breakup of, (4,7) in R1C2, (4,7,8) in R5C2 and (7,8) in R6C2, the digits 4, 7 and 8 can't appear in any of the vacant cells in column C2 further.

If we assume 4 in R1C2, you will find R5C2 and R6C2 both to have DSs (7,8) implying either digit 7, or 8 and no other digit to occupy the two cells. This in fact is a two digit cycle in the two cells. Together with 4 in R1C2, the situation conforms to only digits 4, 7 and 8 occupying the set of three cells involved in the cycle.

Alternately if we assume 7 in R1C2 (this cell has only these two possible digit occupancy), by Digit Subset cancellation we get, digit 8 in R6C2 and digit 7 in R5C2 in that order repeating the same situation of only the digits 4,7 and 8 to occupy the set of three cells.

Effectively, the three digits involved cycle within the three cells and can't appear outside this set of three cells.

This property of a cycle limits the occupancy the cycled digits in other cells of the zone involved (which may be a row, a column or a 9 cell square). This generally simplifies the situation and occasionally provides a breakthrough by reducing the number of possible digits in the affected cells.

A number of Cycles are shown below from a Sudoku hard solution stage:

Cycle (1,2,6) in column C1 is over all three 9 cell squares on the left. It affects only the column C1.

Cycle (3,8,9) in top right 9 cell square is also in row R2, so it should affect both the 9 cell square and R2.

But Cycle (3,6,7) in top right 9 cell square is formed only in the 9 cell squares, it affects only the cells in the 9 cell square.

Can you see another Cycle in row R1 apart from Cycle (1,6)? The second Cycle (3,6,7) is formed by the cells R1C2, R1C3 and the far away cell R1C9. This Cycle affects only the row R1.

Can you say which are the affected areas for Cycle (1,6) in R1?

Two cells of this Cycle belong to row R1 as well as to the top middle 9 cell square. So the Cycle affects two areas, the row and the 9 cell square. **This will be true for any two digit Cycle.**

#### Use of a cycle:

In the example of cycle described above, if a vacant cell R8C2 in column C2 has a possible DS of (1,4), as digit 4 has already been consumed in the cycle (4,7,8) in the column, **only digit 1 can now be placed in R8C2. ***You get a single valid digit 1 for R8C2.*

This is **how a new valid cell is obtained using a Cycle that was not visible otherwise.**

In any hard Sudoku game solution, creating, analyzing and using the pattern of Cycles play a very important role.

### How to find a naked single in a valid cell by Possible Digit Subset Analysis or DSA

Sometimes when we analyze the DSs in a cell, especially in highly occupied zones with small number of vacant cells, we find only one digit possible for placement in the cell. We call valid cell identification in this way as * Digit Subset Analysis*.

For example, if in row R4 we have four empty cells, R4C1, R4C3, R4C6 and R4C9 with digits left to be filled up [1,3,5,9] we say, the row R4 has a DS of [1,3,5,9] that can be **analyzed for validity in each of the four empty cells.**

By the occurrence of digits in other cells if we find * in only cell R4C1* all the other three digits

**as these are already present in the interacting zones of middle left 9 cell square and the column C1, we can say with confidence that**

*3,5 and 9 eliminated*

**only the left out digit 1 of the DS [1,3,5,9] can occupy the cell R4C1.**Remember that,

While

evaluating the valid digit subset or DS of an empty cell,you would analyze not only thein corresponding row, column and 9 cell square, youdigits that are already filledmust include the Cycles present in the three interest zones also.

**This is how we identify a valid cell by Digit Subset Analysis.**

Identifying a valid digit in a cell by DSA is like a bread and butter technique. It is possibly the most heavily used technique after the simplest row-column scan.

Though DSA may not be considered as an advanced technique it often provides a much required breakthrough. So always look for a valid cell by DSA.

An **example of a breakthrough at the late stage of Sudoku hard puzzle solution by DSA** is shown below.

We'll do DSA on cell R7C5. The possible digit subset or DS in column C5 and hence in cell R7C5 is [5,7,9], but the two digits [5,9] both are present in row R7.

So eliminating these two from the three digit DS for R7C5, we get the single valid digit 7 for R7C5 --- R7C5 7.

This is a breakthrough even at this late stage.

### Single digit lock and how to use it in solving an expert Sudoku puzzle

Occasionally, after evaluating valid DSs for a number of empty cells, you may find that,

A single digit appears only in the DSs of two or three cells in a 9 cell square,

in a column or a row,and in no other DSs in the 9 cell square.

This is what we call as **single digit lock.**

If it happens in a row (or a column) inside a 9 cell square, the digit cannot appear in **any other cell in the row (or the column) outside the square***.*

This** eliminates all occurrences of the locked digit from the DSs in the row (or the column) outside the 9 cell square.** Usually it creates a much needed breakthrough. It is a very powerful pattern.

#### Single digit lock - Conditions for single digit lock - how to identify it

Two **conditions for single digit lock pattern,**

- the digit can be placed in only two or three cells of a column or a row, AND,
- the locking cells must also be in SAME 9 cell square.

The third **desired condition** is,

- The lock to be effective, the locked digit should not be present as a single cell candidate in both the adjacent two 9 cell squares through which the locked column or row passes.

The following shows an example of single digit lock of 5 in cells R7C1 and R9C1.

#### How a single digit lockdown is formed

Look at columns C1, C2 and C3 in the bottom left 9 cell square R7R8R9-C1C2C3. Out of 3 empty cells, the cell R7C3 is debarred for placing digit 5 as column C3 has a 5 and it lights up the cell for digit 5.

5 can appear only in two cells in column C1, R7C1 and R9C1 and in no other cell in the 9 cell square or the column C1.

It is locked inside these two cells in C1 and 9 cell parent square.

#### How a Sudoku single digit lockdown is used - What it does

The **locked digit 5 eliminates itself** from the DSs of the other two empty cells R5C1 and R6C1 and a new Cycle (2,3) is created in C1.

Focus again on the bottom left 9 cell square. With Cycle (2,3) in C1, another Cycle (5,9) is formed in the two cells of the 9 cell square. As a result, digit 1 becomes the only digit left and cell R7C3 only cell left for it in the 9 cell square.

Still more happens. With 1 in C3 now, digit 9 now must occupy the cell R6C3.

These two single digit candidates obtained by the single digit lockdown of 5 affects other cells and breaks the bottleneck.

As a strategy, always form a single digit lock as soon as it is discovered.

*You may think, what is the point of it, what would it achieve after all!*

Well, in a similar situation in the process of solving a hard Sudoku puzzle game, the reduced DS in R9C1 formed a cycle (3,7) in column C1 and helped to *pinpoint a valid digit 4 in cell R2C1* and that started a deluge of valid cell finds. *This proved to be the key turning point in the whole game.*

### Expert Sudoku technique of double digit scan

This technique sounds simple, but being aware of its existence and identifying it would always result in an important breakthrough. This digit pattern usually occurs in very hard Sudoku.

We will explain this advanced Sudoku hard technique on the following situation in a Sudoku hard game,

Notice the two **highlighted digits** **[1,6]** appearing in both row R4 and C5. Together these two result in DIRECT FORMATION OF CYCLE (1,6) in central middle 9 cell square.

This is a

double digit scansimultaneously on a row and a column.

Now observe a second set of **highlighted double digits** [3,9] in C5 which DIRECTLY FORMS **TWO CYCLES (4,7,8) AND (3,9)** IN CENTRAL MIDDLE 9 CELL SQUARE.

This is a double digit scan on a single zone of C5.

Finally, with 3 in C4, **R4C4 9 and R4C6 3.**

Together these two double digit scans have produced two valid cells and two Cycles. **It is a major breakthrough** early in the Sudoku hard game.

### Expert Sudoku technique of parallel digit scan for a single digit on a row or a column

A parallel scan is carried out for a specific digit on the empty cells of a promising row (or column). Because of presence of the specific digit in the interconnecting columns (or rows) for all empty cells of the scanned row (or column) except one, the valid cell for scanned digit can be identified as this cell.

The digit pattern and the technique to identify a breakthrough valid cell by parallel digit scan is shown in the figure below,

The parallel scan for digit 6 is done in this case on the empty cells of R1. Out of 4empty cells R1C4, R1C6, R1C7 and R1C9, digit 6 is disallowed in the first two by 6 in top middle major square and disallowed in R1C7 by 6 in C7.

This leaves only the single cell R1C9 where digit 6 can be placed. That becomes the valid cell for digit 6.

Observe that as a result a Cycle (4,7,9) is formed in the rest of the three empty cells in R1.

If you could have identified the Cycle before parallel scan, you could automatically have got the valid cell without parallel scan. That's the interesting property of parallel scan, if you can spot one, you would be sure to find an equivalent Cycle as a result.

To us, valid call by parallel scan is easier and faster.

*To go through the solution of this Sudoku hard once more, click here.*

### More Expert Sudoku puzzles you may like to solve and learn how to solve

The **updated list** of **Solutions to Expert Sudoku **puzzle games:

**How to solve Expert Sudoku puzzle games full list****.**

Expert Sudoku solution strategy and techniques are included in many of the solutions.

*Enjoy solving and learning to solve Expert Sudoku puzzles.*