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I'm trying to write a program that solves sudoku's using a Groebner basis. I introduced 81 variables x₁ to x₈₁, this is a linearisation of the sudoku board.

The space of valid sudokus is defined by:

for i=1,…,81 : F_i=(x_i−1)(x_i−2)⋯(x_i−9) This represents the fact that all squares have integer values between 1 and 9.

for all x_i and x_j which...

National Public Radio in the USA carries Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies. It's an amusing hour on Saturday mornings.

The June edition of the IBM Ponder This website poses the following puzzle:

Assume that cars have a length of two units and that they are parked along the circumference of a circle whose length is 100 units, which is marked as 100 segments, each one exactly one unit long.

A car can park on any two adjacent free segments (i.e., it does not need any extra maneuvering space).