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Example of how to solve Mathematical Mini Sudoku

Let's consider the following Mini Sudoku:

Example of Mini Sudoku

First of all we write down all the possible numbers that could fit into each cell -usually called candidates:

Example of Mini Sudoku with candidates

After that we consider the cells indicating odd to analyse the possibilities. Since they only have two candidates, these cells can be solved faster and more easily than the rest.

See then the 2nd cell of the 1st row and the 1st cell of the 2nd row. We choose the latter because the total sum of the row is 10, the lowest value compared to the rest of results (except the one in the 3rd column). By doing so we reduce the range of possibilities.

When considering this value we will soon realise that candidate 9 does not match because there are still two numbers to be added up and the result would always be higher than 10. Therefore, the only number that fits would be 1. By elimination, the number in the other cell indicating odd has to obviously be 9.

We have already found two numbers!

Example of Mini Sudoku with 1 and 9 solved

The next row to be analysed would be the 2nd because the result of the sum is the lowest and we also have a cell that is already solved.

We need a sum that equals 10 adding up number 1 and the possible numbers in the other two cells. Number 8 does not match because we would need number 1 in the following cell and this is not possible because we need a prime number and we would use 1 twice. So we can reject candidate 8.

Numbers 4 and 6 could be valid because we would have 9 after adding up 5 and 3, respectively. There are no more options, so we can reject candidates 2 and 7 for the 3rd cell:

Example of Mini Sudoku rejecting candidates

Now we analyse the 1st row because we already have number 9. We need a sum that equals 15, so we have to get 6 when adding up the numbers in the other two cells.

After a quick look at the candidates we would realise that the only option possible is to pick 4 for the 1st cell and 2 for the 3rd. Any other combination would have a result higher than 6. Therefore, we have found two more numbers that will also be rejected as candidates from the rest of the cells:

Example of Mini Sudoku with 2 and 4 solved

Now we can see that the only candidate left in the cell of the middle is 6, so we have found another number! We can also reject it as candidate in the only cell indicating even:

Example of Mini Sudoku with 6 solved

In the 2nd cell of the 3rd row there is also one candidate left, number 8. So we have found the last even number:

Example of Mini Sudoku with 8 solved

In the 2nd row and the 1st column we have two numbers already solved and only one blank cell. What we have to do is to take the result of the total sum and subtract such numbers. Number 3 will be the correct candidate for the 2nd row (10-1-6=3) and number 7 will be the one for the 1st column (12-4-1=7):

Example of Mini Sudoku with 3 and 7 solved

There is only one blank cell now! Here it fits the only number that is left, number 5.

Example of Mini Sudoku with 5 solved and finally completed

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