PUZZLE TECHNIQUES

BETWEEN 1 & 9 SUDOKU (EXAMPLE)

Below we will discuss step by step the solution of a Between 1 & 9 Sudoku using an example (= puzzle 10). In this variant, also called sandwich sudoku, there are numbers above and on the left side of the sudokugrid which represent the SUM of the digits between 1 and 9.

First you can look HERE for our overview with all possible combinations with the numbers 5 - 35 and their distribution over 2 to 6 squares. The digits 2, 3, 4 cannot be divided into more than 1 cell.

SOLVING SANDWICH SUDOKU (puzzle 10)

We will now show the steps to solve a Between 1 and 9 Sudoku. We use a sandwich sudoku that we have developed ourselves. It's puzzle 10 on our website.

Step 1

We focus on rows and columns that already contain numbers and on large SUMS in the frame such as 29 (= row 2) and 31 (= column 1) in this example

Step 2

We first look for the missing 1s and 9s by excluding cells (= by coloring them) where these digits can NOT be found. Box 3 contains digit 9 in box R2C8. The sum number of column 8 is 0. So 1 is in R1C8 or R3C8. We can therefore exclude the other cells in box 3 by coloring them.

In column 1 we have 31 as the sumnumber. This means that the digit 4 is outside the 19-group. There are 2 possibilities for digit 4: R1C1 or R9C1. So we can exclude five cells in column 1.

In row 2, with 29 as the sum number, digit 6 is outside the 19-group. Here we also have 2 options: 6 in R2C9 or 6 divided into 2 and 4. This means we can also exclude 5 cells in row 2.

Finally, we can also exclude R1C4 because sum number 0 of column 4 indicates that 1 and 9 are below each other.

Step 3

For the sake of clarity, we give the new cells that we exclude a different color so that you can see the difference with the previous image.

It gets a bit complicated here, but you'll succeed. Sum number 2 in column 6 means that we have 129 or 921. This combination is NOT possible in box 2, because then we cannot place 1 in R1C8 or R3C8. So we can also exclude these cells.

In column 5 we have 15 and therefore at least a 19-group with 2 cell between, eg 1789. So there is certainly a 1 or 9 in R3C4.

In column 4 we have sum number 0 and can therefore also place the 19-combination in R4C4. In column 4 we can therefore exclude everything under 19.

In row 4 the sum number is 20. We need a minimum of 3 cells and can therefore exclude 2 cells in row 4.

In row 4 we can only make 20 by placing a 19combination in R4C9. Below that we can exclude 2 cells because we require a minimum of 2 cells for sum 14 of column 9.

Step 4

We already have 1 and 9 in row 3, so we can exclude cells R1C3, R3C2 and R3C3 in box 1 and R3C5 in box 2.

In R3C8 we can now place 1 and as a result we can change all 19-combinations in 1 or 9. In addition, we can exclude R1C8.

We are now moving to row 4 where we can exclude R4C5 and R4C7.

If we now look at column 5, the sum of 15 can contain at most 4 cells, so that we can exclude the 3 cells at the bottom in box 8.

We can exclude R8C2 because if we place 1 or 9 here, then we cannot satisfy sum 4 of row 2.

We can also color R7C2 because we know the following about box 7:

• Due to the sum of 20 of row 9, we certainly have a 1 or 9 in R9C1, R9C2 or R9C3.
• Due to sum 4 of column 3 we certainly have a 1 or 9 in R7C3 or R8C3.

Step 5

We look at column 5 to place 941 or 149 through exclusion:

• It is not entirely possible in box 7 as we still have to place 1 or 9 in R8C1 or R9C1 for sum 31 of row 1.
• Digits 1 or 9 cannot be entered in R6C3 either, because then in box 4 there is no place left where we can place 1 or 9.

We can place 1 and 9 in box 4 and exclude the remaining cells.

We can place 951 in row 6.

We can place 921 in box 8.

Then 9 and R9C1 and the rest are easy to place.

Step 6

In column 5 we need 4 cells to make a sum of 15. So 2346 must be divided between these cells.

What remains for column 5 is 578 in box 8.

In box 8, column 7, we can now place 346.

Something very nice is now visible in row 9. We are now looking at the outside group. This means: 20 is in the inside group and 15 is the outside group, which is completely in box 9. In box 9 we have to form 15 without 5 and 4 already there. Only 267 remains as a combination.

In box 9 row 7 we can now also place 38 in the remaining cells.

Step 7

In row 7 we get 1479 due to the influence of the 38 pair and the 26 pair in the 1st cells.

R9C2 is the only space for digit 4 and R2C4 is the only space for digit 5.

We can place pairs 27 and 34 in box 5.

It is also clear in column 5 where we can place 2 and 6.

Step 8

We now look at sum 18 in column 2 with 378, 468 and 567 as combinations. 468 is dropped because we already have a 4 in column 2. 567 is also dropped because we already have a 6 in rows 2, 3 and 4. This leaves 378 as the only combination.

In R8C2, 5 and 8 now come in R8C5 and 5 in R9C5 and 8 in R9C3.

In row 1 we now know where we can place 6 and 8.

In column 6 we can place 8 and 47 pairs.

Step 9

In row 3 we can only place 2 and 5 in R3C1 and R3C3.

We look at row 3 where we have an outside group of 22 with 4 cells where 2 and 5 certainly belong to. So 7 and 8 are left over for R3C2 and R3C9.

As a result, we can place 4 and 7 in columns 6 and 8 and 3 in row 7.

In column 3, 7 can only be used in row 8.

The rest of the numbers follow automatically.

Step 10

In column 5 there is now clarity about 3 and 4.

We can place 4 in R2C7.

In row 4, 2468 is the only possible combination. So it is easy to place 8 and 2.

In row 5, R5C9 is the only place left for digit 4.

This means that the digit 5 in column 9 can only be used in R1C9.

Step 11

These digits can now be entered based on basic sudoku techniques.

Step 12

Here too, the missing digits can be filled in with simple sudoku methods.

I hope you learned new techniques with our step by step discussion of a Between 1 and 9 sudoku. We will create more sandwich sudoku in the near future.