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Mr. Vincent Glover

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What is Kakuro?


The kakuro puzzle (analog Web Sudoku), also known as cross-sums, consists of blue and white squares. Several white cells following each other (vertically or horizontally) form a block. To the left of each horizontal and above each vertical block is a blue square containing the sum of the block digits. It is required to fill in all white cells with numbers from 1 to 9 so that the numbers in the blocks do not repeat.

Please also note that in horizontal or vertical lines - numbers (if they are in different blocks) can be repeated! It is also worth noting that regardless of size, kakuro is always filled with numbers from 1 to 9 (unlike online Sudoku).

An example of Kakuro's solution algorithm


Consider the bottom-right kakuro block (horizontally, in the picture on the right). The block consists of two cells with the sum of 4 digits. Let's write down all combinations of two digits that add up to 4: 1 + 3, 2 + 2, 3 + 1. 2 + 2 cannot be used, since the numbers in the block should not be repeated, only 1 + 3 and 3 + 1 remain.

Next, consider the adjacent vertical block. Two digits, sum 10. For such a sum, quite a few different combinations are possible. However, we have already found out that in the lower cell there can be only 3 or 1, and, therefore, in the upper one - only 7 or 9.

Now let's pay attention to a long horizontal block of 8 digits with a sum of 36. The sum of all nine digits is 1 + 2 + ... + 9 = 45. This means that the number 9 cannot be present in the block under consideration (45-36 = 9). Thus, only 7. You can immediately put the numbers in the blocks considered earlier in the cell with candidates 7 and 9. (10-7 = 3, 4-3 = 1)