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Sudoku solving algorithms. A typical Sudoku puzzle. A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
Mathematical context. The general problem of solving Sudoku puzzles on n2 × n2 grids of n × n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell.
Many Sudoku solving algorithms, such as brute force-backtracking and dancing links can solve most 9×9 puzzles efficiently, but combinatorial explosion occurs as n increases, creating practical limits to the properties of Sudokus that can be constructed, analyzed, and solved as n increases.
Optimal solutions for the Rubik's Cube. Optimal solutions for the Rubik's Cube are solutions that are the shortest in some sense. There are two common ways to measure the length of a solution. The first is to count the number of quarter turns. The second is to count the number of outer-layer twists, called "face turns".
Try Sudoku. The logic puzzle has simple rules, and is easy to learn. Worked out your body enough and want to move on to your brain? Try Sudoku. The logic puzzle has simple rules, and is easy to learn.
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that ...
The Rubik's Cube is a 3D combination puzzle invented in 1974 [ 2][ 3] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, [ 4] the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, [ 5] and then by Ideal Toy Corp in 1980 [ 6] via businessman Tibor Laczi and Seven Towns ...
The CFOP method (Cross – F2L – OLL – PLL), also known as the Fridrich method, is one of the most commonly used methods in speedsolving a 3×3×3 Rubik's Cube. It is one of the fastest methods. This method was first developed in the early 1980s, combining innovations by a number of speed cubers. Jessica Fridrich, a Czech speed cuber and ...
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