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To solve a Killer Sudoku puzzle, you must use both known and unknown numbers on a line or in a column to deduce the value of other combinations.

**Unique per row, column and block:**Killer Sudoku shares the basic rules of regular Sudoku, where numbers must be unique within a row, column, and block.**Elimination:**By knowing that a number is already present in a certain field, you can eliminate it from other fields in the same row, column, or block.**Caution with Pencilled Numbers:**While you can use pencilled numbers to eliminate possibilities within a block, be cautious when using them to eliminate possibilities in rows or columns, as it may lead to incorrect deductions.

*In part two of a three part series on Killer Sudoku, we'll talk about row and column matching. Yesterday, we discussed basic strategies. We're finishing with an advanced counting strategy tomorrow.*

A Killer Sudoku shared its basic rules with the regular Sudoku puzzle.

One of the rules of a Killer Sudoku puzzle is that **a number must be unique on a horizontal row, in a vertical column and inside a block**.

Let's look at how we can use this rule to solve a Killer Sudoku puzzle.

If you know that a number in a field is already definite, you can **eliminate this number from all fields in that row**, column or block.

Have a look at this situation here. The **8 **was given by the puzzle itself, the **7**, **9 **and **pencilled numbers** have already been deduced in this post on basic strategies.

*With an 8 in the bottom right corner, the 8 can no longer appear in any field on the bottom row.*

So, the **8 **is already on the **bottom row **in the right block.

That means in the **left block**, we can already **eliminate the 8 on the bottom row**. This will cross off both of the fields in the combinations with sum 9.

*With the 8 used in combination 14 of the middle block, the 8 is no longer allowed in the middle line of the left block.*

In the **middle block**, we have already deduced that the combination of **sum 14** will be** 6 + 8**.

Because of this, this will eliminate the **8 **as an available number on the whole **middle row**. We have now **ruled out 1 + 8 **as an eligible combination for both combinations with sum 9.

*The 8 is only allowed of the top row in the left block. As 8 isn't used in a combination with sum 7, it must go in the combination with sum 11.*

That leaves the top row of the left block.

The top row is made up of 2 combinations: a full **combination of sum 7 **and one field of a **combination of sum 11**.

Obviously the 8 won't fit in the combination of 7, which automatically means that the 8 will have to go in the **top field** in the **combination of 11**.

Now, while solving the middle row of the left block, we know knew there couldn't be an 8. Why? Because

- in the middle block, the 8 is
**already used in the combination of 14**; AND - a number can
**only appear once on every row**.

This is the basic Sudoku rule.

Be careful though: **you can't use a vertical combination to exclude a number on a horizontal row!**

Let's take a look at this example. It's the same puzzle as before. We filled in the **8 **and added the **3 **to make up a **sum of 11**. We also deduced the **combination of 7 **in the middle block to be **2 + 5**.

*You can't take a vertical combination and use it to deduce a horizontal row... or can you?*

In the left block you might be tempted to use this 2 + 5 combination to rule out numbers 2 and 5 for both the combinations of 9. DON'T!

Even though you know that the bottom field of that combination of 7 is a 2 or 5, it's exactly that: **2 OR 5**.

If it's a 2, the 5 can be used in the left block. Similarly, if it's a 5, the 2 can be used in the left block. Even 'worse': the 2 and 5 can still go in the bottom row, **leaving both 2 + 7 and 5 + 4 combinations valid** for the left block.

There is an exception to the rule which does let you use pencilled numbers in a different orientation. Let's have a look at the top row.

We know a **combination of 7** can be made up of **1 + 6**, **2 + 5** or **3 + 4**.

**3 + 4 is a no go**, as:

**the 3 is already used**in the combination of 11; AND- a number must be
**unique within a block**.

Can we use **2 + 5**? We just said that you can't exclude a combination on a row based on a vertical combination in another block, right?

In this case, even that vertical combination affects this horizontal combination for 7. Why?

- If the combination in the middle block has the 2 on top and 5 below, it
**excludes 2 from that row**. In the left block, we can no longer use 2 + 5. - If the combination in the middle block has the 5 on top and 2 below, it
**excludes 5 from that row**. In the left block, we can no longer use 2 + 5.

Regardless of the order in which the 2 + 5 combination is used, **either 2 or 5 are ruled out**. As the 2 and 5 are **both essential** to make up a combination of 2 + 5 (duh), this **excludes the 2 + 5 combination for sum 7 **in the top row of the left block.

This leaves **1 + 6** as **the only possible combination**.

Now, of course this means that for the both combinations of 9 we should use the **2 + 7** and **4 + 5**. In this case, we don't know which combination is used for which sum.

What we can say, is that the **7 is already used in the bottom row**. That means for the combination of 2 + 7, the order will be **7 on top and 2 below**.

Also, see that 14 in the right block? In the basic strategy post we already pencilled in the combination **5 + 9**. That means we know the 5 can't go on that row any more, making the combination of 7 in the middle block **5 on top and 2 below**.

This places a number 5:

- On the top row, in the middle block; AND
- On the middle row, in the right block.

The only row left for a 5 is the bottom row, which means the combination of 4 + 5 will have **4 on top and 5 below.**

*With all but one field pencilled in, we are ready to fill in the final number on that middle row.*

To conclude this post, we have defined or pencilled in the middle row completely, apart from **the field on the far right**.

If we check all the numbers, only the **number 1 is missing in this row**. This makes it easy: the **1 **can be filled in on the far right field. It will sit together with the 8 in the combination of 3 for sum 15.

And of course, that means the third field of this combination for sum 15 will be...?