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Multi-dimensional Sudoku Puzzles Set to Get Tougher
Dr Paul Newton and Stephen DeSalvo of the University of Southern California in Los Angeles have published their report on Sudoku matrices in the Proceedings of the Royal Society A.
"I think it will help develop multi-dimensional Sudoku puzzles, and answer questions about how to give the initial [clues] in order to create a hard, but still solvable Sudoku puzzle," ABC Science quoted Newton, as saying.
A Sudoku puzzle solution comprises of a 9 x 9 matrix of numbers from 1 to 9.
Each number should only appear once along any row and once down any column, as well as only once in each of the three 3 x 3 sub-blocks that make up the matrix.
There is believed to be about 1021 different matrices.
Newton and DeSalvo created a "representative sample" of about 10,000 matricies and compared them to randomly-generated matrices.
They discovered that Sudoku matrices are more random than randomly-generated arrays.
According to Newton, this is surprising since one would expect the more constraints you have on a matrix, the less random it will be.
But he points out that in a randomly generated square, you may end up with a matrix made up entirely of one number, which is something you could never get given Sudoku's rules.
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