This is an example of a completed Kakurasu puzzle. To solve a Kakurasu puzzle,

1. The black cells in each row must add to the total given on the right.
2. The black cells in each column must add to the total given on the bottom.

The values on the top and left side of the puzzle give the value of each cell.

1. Looking at the first row, we have 1 + 4 + 6 + 7 = 18.
2. Looking at the seventh column, we have 1 + 2 + 3 + 4 + 6 + 7 = 23.

This is an example of a starting Kakurasu puzzle. We always start by looking at the small and large totals. In this case, we have a horizontal total of 3 for one of our rows. To have a total of 3, we know that the 4, 5, 6, and 7 cells can't be filled, i.e. we can insert a dot in cells 'A', 'B', 'C', and 'D'.

We can also look at the larger totals. In this case we have rows with totals of 23 and 24. There are a few different ways to make 23,

• 1 + 2 + 3 + 4 + 6 + 7 = 23
• 1 + 4 + 5 + 6 + 7 = 23
• 2 + 3 + 5 + 6 + 7 = 23

All of these different ways to make 23 include 6 and 7, i.e. we can fill in cells E and F.

We can apply a similar argument to the bottom row with a total of 24, i.e. we have to use 6 and 7 to make 24, and we can fill in cells G and H.

The last column in this puzzle has a total of 23, but we know that we can't use the 5 in this column. This leaves only one way to make 23, i.e. 1 + 2 + 3 + 4 + 6 + 7 + 8 = 23, and we can fill in cells A, B, C, and D.

Our second row has a total of 7, and we have just filled in cell B, i.e. we already have a total of 7 for this row. This means the rest of this row must be empty.

Column 6 has a total of 18, but we already have some cells filled in for this column. With the cells remaining there is only one way to reach a total, and that is 1 + 4 + 6 + 7, i.e. cells A and B must be filled.

The bottom row has a total of 24, and we already have 6 + 7 = 13. This leaves us needing 24-13=11 from the remaining cells, and there are only a few ways we can do this,

• 1 + 4 + 5 = 11
• 2 + 3 + 5 = 11

Both of these ways include the number '5', i.e. cell C must be filled.

We can also look at the third column, with a total of 9. There are many ways to reach a total of 9 for this column, but since we can't use the '2' for this column, none of them include '7', i.e. cell D must be empty.

Looking at the bottom row, there is only way to make a total of 24 with the combination of filled and empty cells here, 2 + 4 + 5 + 6 + 7 = 24. Cell A must be empty, and cells B and C must be filled.

We can also look at the 5th column, we already have a total of 7 for this column, and some cells are not available to us. The only way to make 10 for this column is 7 + 3 = 10, i.e. cell D must be filled, and the remaining cells in this column must be empty.

We are now halfway through this Kakurasu puzzle, and we have covered all of the techniques needed to solve these types of puzzle.