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Linear Programming and Algorithms for Communication Networks by Eiji Oki

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Chapter 9

Mathematical puzzles

This chapter presents mathematical puzzles that can be tackled by integer linear programming (ILP). They are the Sudoku puzzle, a river crossing puzzle, and a lattice puzzle. The ILP formulations and solutions by GLPK are presented. For the river crossing puzzle, the shortest path approach is also introduced to solve the problem.

9.1 Sudoku puzzle

9.1.1 Overview

Sudoku is a logic-based, combinatorial number-placement puzzle [1]. First published in the United States in 1979, this puzzle was designed by Howard Garns, an architect from Indiana. In its first publication by Dell Magazines, it was known as Number Place. The name “Sudoku” was introduced when the puzzle was published in Japan by Nikoli, a Japanese publisher ...

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