Kakuro 10x10 #4 Very Hard

Online solution rules Kakuro 10x10 #4 Very Hard

Kakuro or Kakuro is a kind of logic puzzle, which is often called the mathematical transliteration of a crossword puzzle. Kakuro's puzzles are featured regularly in many math and logic puzzle publications.

Standard game and terminology

The canonical Kakuro puzzle is played in a grid of filled and shaded cells, "black" and "white" respectively. Apart from the top row and the leftmost column, which are all black, the grid is divided into "records" - lines of white cells - by black cells. Black cells contain a diagonal slash from top left to bottom right and a number in one or both halves, so that each horizontal entry has a number in the black half-cell to its right, and each vertical entry has a number in the black half-cell immediately above it. These numbers, borrowing the terminology of crossword puzzles, are commonly referred to as "clues".

Puzzle problem - insert a number from 1 to 9 inclusive in each white cell so that the sum of the numbers in each entry matches the clue associated with it, and so that no number is duplicated in any in one entry. It is the lack of duplication that makes it possible to create Kakuro puzzles with unique solutions, which means that solving the Kakuro puzzle involves more careful study of combinations compared to Sudoku, which focuses on permutations. There is an unwritten rule for creating Kakuro puzzles that each clue must contain at least two numbers that add up to it. This is because including a single number is mathematically trivial when solving Kakuro's puzzles; one can simply ignore the number entirely and subtract it from the hint it indicates.