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Mathematical Problems of Sudoku Puzzle and their Relationship

Jahani, Zohre | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47082 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahmoodian, Ebadollah
  7. Abstract:
  8. The Sudoku puzzle is played on a 9 × 9 grid which is divided into nine boxes each with 3 × 3 cells. Initially, some digits between 1 and 9 are given on the grid as the clues. Generalized Sudoku (a table of n2 by n2 that includes n2 blocks with n cells and in each of its rows, columns and blocks has all numbers from 1 to n2 appeared once and only once) can be considered too. Millions of people around the world are tackling one of the hardest problems in computer science without even knowing it. The first such puzzle appeared in the May 1979 edition of Dell P encil P uzzles and W ord Games and, according to research done by W ill Shortz, the crossword editor of the N ew Y ork T imes, was apparently created by a retired architect named Howard Garns. It was published continuously from 1986 in Japan. Solving a Sudoku puzzle requires no math, not even arihmetic. Even so, the game poses a number of intriguing mathematical problems. In fact, no operation including addition or multiplication helps in completing a grid. The logic game Sudoku is a miniature version of a longstanding mathematical challenge, and it entices both puzzlers, who see it as an enjoyable plaything, and researchers, who see it as a laboratory for algorithm design. Since Sudoku has just one condition more than Latin square, we can discuss the problems of Latin square for Sudoku too. Latin squares and their critical sets are used in cryptography so Sudoku is expected to be used in this way too. Although, Sudoku is used in Neural Network, Coding, Teaching chemistry, etc. In this thesis, we try to study some problems raised in Sudoku mathematically
  9. Keywords:
  10. Sudoku ; Critical set ; Latin Square Method ; Sudoku Graph

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