Since there are $5!$ permutation matrix, I have managed to create $(5!)^2 = 14400$ valid patterns this way, although each pattern appears 5 times, so only 2880 of them are distinct. The resulting pattern $P'$ can be represented by $R \times P \times C$, where $R$ and $C$ are two permutation matrices indicating the rows and columns to permutate, respectively. The size of the returned tensor remains the same as that of the original. I've realised that I can build valid patterns by permutating the rows and columns of the predefined pattern, as these operation preserve the number of different colours in each row or column. observations in a dist object, the rows and columns of a matrix or ame, and all dimensions of an array given a suitable serpermutation object. PyTorch torch.permute () rearranges the original tensor according to the desired ordering and returns a new multidimensional rotated tensor. The advanced playing mode has no predefined pattern, so you can come up with your own, while respecting the constraint that no colour appears twice in each row or column. permutation index followed by the elements of the row being randomised. For the normal mode, the tiles must be placed following a predefined pattern, which can be seen here and that I represent with the following matrix $P$, where each letter represents a different colour: of matrix are designated by numeric value called. In the boardgame Azul, your goal is to complete as much as possible of a $5\times5$ board by placing 25 tiles of 5 different colours (5 tiles of each colour) so that no colour appears twice in a row or column.
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