PUZZLE TECHNIQUES

MYSTERY SUDOKU (PUZ 1)

Below we will explain step by step the solution of a Mystery Sudoku using an example (= puzzle 1). You can go to our page Mystery Sudoku and solve this puzzle online or other mystery sudokus.

HOW TO SOLVE A MYSTERY SUDOKU

A Mystery Sudoku is a new variant that I came up with. When we look at an example, then we notice two things simular to a sum frame sudoku or sandwich sudoku:

• There are sum numbers outside the grid.
• In the grid there ar no or a few numbers.

MYSTERY SUDOKU RULES

In each solved sudoku we have the digits 1 to 9 in each row, column or box. In a mystery sudoku the extra rule is that at the start one of the 9 digits is the mystery digit. If for example 2 is the mystery digit, then we have to find the 9 locations of digit 2 using the sun numbers outside the grid and solve the complete sudoku on the way.

Step 1 - Location of the Mystery Digit

The only thing we know is that the middle cell ALWAYS contains the mystery digit. So I desginate it as one of the 9 locations of the mystery digits using a color.

Step 2 - The meaning of the sum numbers

In a sum frame sudoku the sum numbers give us the total of the first three digits. In a sandwich sudoku the sum numbers give us the total of the digits between 1 and 9.

In a Mystery Sudoku the sum numbers give us the total of 3 digits that are connected with the mystery digit. Look at our example!

• Sum number 16 = total of A, B and C.
• Sum number 9 = total of A, D and G.
• Sum number 23 = total of C, F and I.
• Sum number 19 = total of G, h and I.

You will notice that there is an overlap. In our example digit A is a part of sum number 16 and of sum number 9. This informatie will help us at lot to solve these puzzles.

What do we know with this information?

• If 1 is the mystery digit (=middle cell), then A, D and G can only be 2, 3 or 4.
• If 2 is the mystery digit (=middle cell), then A, D and G can only be 1, 3 or 5.

Let's move on

Step 3 - Four extra Locations of the Mystery Digit

When we analyze the sum numbers, then we will ALWAYS find 4 sum numbers "0". Does this mean something? Of course it does.

if you have a "0" as sum number, then the total of 3 digits above, below, at the left or at the right of that mystery digit is "zero". This can only mean one thing. You have find the location of the mystery digit of that row or column.

So at the start we can immediately mark 5 locations of the mystery digit.

Step 4 - Look for more Locations of the Mystery Digit

We can use classic sudoku techniques to find extra locations of the mystery digit. To keep it clear, I limit myself to boxes with a maximum of 2 candidates.

Until now we have 6 exact locations of the mystery digit and 2 boxes with 2 candidates.

Step 5 - Look for Sum Numbers with 1 combination

When we want to divide 23 in 3 digits, then 6-8-9 is the only possibility.

Step 6 - Look for digit numbers close to each other

There is an overlap between mystery digit A and B. Below cell A two cells must have a total of 13 and above cell B three cells must have a total of 17. The difference between 17 and 13 is 4 and this is the value of the cell that isn"t part of the overlap. Pfff! I never said it would be easy!

Because we now have number 4 in this box, there is only 1 combination (23) for the sum number 5 above cell A.

The left sum number for cell B is 20. We already have 4, so this leaves us with (79) as the only combination for the remaining 16.

Above number 4 and at the right we need 13 as the total of 2 cells. We can only choice between 58 or 67.

There is only 1 cell where we can enter digit 9.

Finally we can determine the value of the mystery digit. Number 1 is the only possibility!

Step 7 - Enter the value of the mystery digit.

We enter the value of the mystery digit and look if this helps us in finding more digits.

Now there is only 1 possible combination for sum number 9 at the left side of the middle cell.

The cell below the middle cell of the grid has sum number 19. If we would use the maximum available numbers (left=4 and right=9), then we would need digit 6 or higher. That is why we place 7 in the cell below the middle cell and 5 above.

Step 8 - Look at other mystery digits.

When we look closely at the 4 sum numbers of the mystery sudoku in the middle of the grid, then we can eliminate some candidates.

Because we have number 6 in row 5, we can add candidates for the mystery digit in column 1.

Step 9 - Don't forget the basic sudoku rules.

When we look at digit 7 in row 5 and 6, then we can find the place for digit 7 in row 4.

At the right side of column 8 we have 19 as sum number. To reach that number we need an 8 and row 4 is the only place where we can enter it.

In column 5 we have 46 as the only possible combination to create sum number 10.

We add 47 in column 6.

We add 236 in column 7.

Step 10 - Time to find the location of a next mystery digit.

If we would place the mystery digit in row 8 of column 4, then the sum number at the right side would be 15. In column 5 we only have 2, 3, 8 and 9 left. It is possible the make 15 with 3 of those numbers. So the mystery digit must be entered in row 7 of column 4.

Looking at the sum numbers we can add more numbers.

Step 11 - We can find the last mystery digits.

Using classic sudoku rules we find the mystery digit of row 3 and 8.

We can place numbers 5 and 6 in row 7 and 9. This helps us to find more numbers around the mystery sudoku in row 1.

We can place numbers 5 and 6 in row 7 and 9. This helps us to find more numbers around the mystery sudoku in row 1.

Step 12 - Almost at the finish.

Now can finish the rest of the mystery sudoku using the information of the sum numbers and the classic sudoku techniques.