with Tags:
mathematics
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## Solving the hardest Sudoku - part 1
Do you know the hardest Sudoku problem? Do you know the best way to solve it? Before answering these questions, let me remind you of what the Sudoku puzzle is about in case you haven't read a newspaper in the last decade (adapted from wikipedia ): The objective is to fill a 9×9 grid with digits so that the digits in each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also called ""blocks") are pairwise different. The puzzle setter provides a partially completed grid, which... [More]
Tags: constraint_programming mathematical_optimization optimization analytics sudoku mathematics |

## Centers of Polygons in OPL
Ryan J. O'Neil has written an interesting post on centers of polygons . Reason I'm blogging here is that he also asks an interesting question for the case where the polygon is a rectangle. Before looking at rectangles, let's define the general problem. There are several definitions of the center of polygons, and we'll use the one used by Ryan: it is the center of the largest circle contained by the polygon. It is called the Chebyshev center of the polygon. Here is an example used by Ryan.... [More]
Tags: mathematics optimization analytics mathematical_optimization |

## Un Peu de Math avec CPLEX
There is one thing I didn't disclose in my previous post (Un Peu de Math) on the Analytic Bridge Mathematical Competition : I used CPLEX to refine and validate various hypothesis. As usual, my first try wasn't very convincing, and I had to rely on better understanding of the problem to solve it efficiently. Let me start with a statement of the optimization problem to be solved. A permutation x is a function such that x(i) is in the set {0,1,...,n-1} for all i in that set.... [More]
Tags: mathematics modeling |

## Un Peu de Math
The following was triggered by a mathematical problem proposed by Vincent Granville. The problem was to compute the maximum value q(n) of a function related to the well known metrics Spearman's footrule , or L1. This would then be used in a new stat isti cal corr elat io n based on ranked variables that would be very useful for Big Data applications. I'll refer readers to Granville's article for more details. At first sight this seemed quite diffficult, and Granville launched a... [More]
Tags: analytics big_data mathematics |