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Grades

Enter digits into the grid, such that no two horizontally, vertically or diagonally adjacent cells contain a digit. The numbers above and to the left of the grid give the number of digits in each row and column, while the numbers below and to the right of the grid show the sum of the digits in each row and column.

Example

In this example, we have to place six digits. We can start with the bottom row. In this row, we need to place a single digit, and the sum has to be 9, so we have to place a 9. The only column where we can place it is the first, because in the other columns the sum is smaller than 9. Similarly, in the third column we need to place a single 1. The only row where we can place it is the first, because the other rows all have a single digit with a higher value.

Now we still have to place the remaining four digits. These have to be in four different rows and columns, so we already know their values. We can place the 8 and the 2, since in both cases there is only one row and column that need that value. Now there are still two rows and columns left that both need a 5. But we can place them only in one way, because otherwise one of them would be adjacent to the 1.


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