# What is Sumdoku?

Sumdoku - Also known as killer sudoku or killer sudoku. In this type of free online Sudoku puzzle, the numbers are arranged in the same way as in classic Sudoku. But on the field there are additionally colored blocks, for each of which the sum of the numbers is indicated. Please note that sometimes numbers in these blocks can be repeated!

## How to solve sumdoku?

Consider a sumdoku (pictured on the right, analog web Sudoku). To solve it, remember that the sum of the numbers in any row, any column and any small rectangle is the same. For our case, this is 1 + 2 + 3 + ... + 9 + 10 = 55. For a 9x9 sumdoku it would be 45.

Let's pay attention to the blocks highlighted in gray. They almost completely (except for one number) cover the two lower rectangles. Let's calculate the sum of the digits in all marked blocks: 13 + 8 + 13 + 15 + 13 + 7 + 14 + 12 + 5 = (13 + 13 + 14) + (13 + 7) + (12 + 8) + (15 + 5 ) = 40 + 20 + 20 + 20 = 100.

So, the sum of the digits in the marked blocks is 100. But if we take the two lower rectangles completely, then the sum of the digits in them should be 55 + 55 = 110. This means that the only unmarked cell contains the number 10.

As you can see, constantly solving sumdoku, you masterfully master arithmetic. You can, of course, use a calculator, but this dark and slippery path is not for real samurai;)

Consider now the blocks highlighted in the figure on the right. They cover one penultimate horizontal line of the online Sudoku and two "extra" cells. Let's calculate the sum of digits in blocks: 13 + 8 + 15 + 13 + 10 + 14 = (13 + 13 + 14) + (10 + 15) + 8 = 40 + 25 + 8 = 73. But we know that the sum of digits in horizontal lines 55, which means that you can find out the sum of the digits in two "extra" cells: 73 - 55 = 18.

Let's write down all possible combinations of numbers in these "extra" cells: 10 + 8, 9 + 9, 8 + 10. 9 + 9 - we exclude, since the cells are located on the same horizontal, 10 + 8 and 8 + 10 remain. But if you put 8 in the first "extra" cell, then in the penultimate horizontal you will get two fives, and the numbers in the horizontal lines should not be repeated. Thus, we get that in the first "extra" cell there can be only 10. We place the rest of the obvious numbers at once.