Suppose we want to construct a uniform matrix of n+1 rows and n*n columns. The definition of a uniform matrix is that each row has n*n non-repetitive natural numbers (1 to n*n), and each row is equally divided into n intervals. There are n numbers in each interval, and any two intervals of different rows have an intersection of 1.↵
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Find a matrix of n=100.↵
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The following are the examples:↵
n = 2 :↵
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[[1, 2],[3, 4]]↵
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[[1, 3],[2, 4]]↵
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[[1, 4],[2, 3]]↵
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n = 3 :↵
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[[1, 2, 3],[4, 5, 6],[7, 8, 9]]↵
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[[1, 4, 7],[2, 5, 8],[3, 6, 9]]↵
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[[1, 5, 9],[2, 6, 7],[3, 4, 8]]↵
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[[1, 6, 8],[2, 4, 9],[3, 5, 7]]↵
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n = 4 :↵
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[[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12],[13, 14, 15, 16]]↵
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[[1, 5, 9, 13],[2, 6, 10, 14],[3, 7, 11, 15],[4, 8, 12, 16]]↵
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[[1, 6, 11, 16],[2, 5, 12, 15],[3, 8, 9, 14],[4, 7, 10, 13]]↵
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[[1, 7, 12, 14],[2, 8, 11, 13],[3, 5, 10, 16],[4, 6, 9, 15]]↵
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[[1, 8, 10, 15],[2, 7, 9, 16],[3, 6, 12, 13],[4, 5, 11, 14]]↵
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Can you give me an idea? thank you!↵
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↵
Find a matrix of n=100.↵
↵
The following are the examples:↵
n = 2 :↵
↵
[[1, 2],[3, 4]]↵
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[[1, 3],[2, 4]]↵
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[[1, 4],[2, 3]]↵
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n = 3 :↵
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[[1, 2, 3],[4, 5, 6],[7, 8, 9]]↵
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[[1, 4, 7],[2, 5, 8],[3, 6, 9]]↵
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[[1, 5, 9],[2, 6, 7],[3, 4, 8]]↵
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[[1, 6, 8],[2, 4, 9],[3, 5, 7]]↵
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n = 4 :↵
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[[1, 2, 3, 4],[5, 6, 7, 8],[9, 10, 11, 12],[13, 14, 15, 16]]↵
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[[1, 5, 9, 13],[2, 6, 10, 14],[3, 7, 11, 15],[4, 8, 12, 16]]↵
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[[1, 6, 11, 16],[2, 5, 12, 15],[3, 8, 9, 14],[4, 7, 10, 13]]↵
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[[1, 7, 12, 14],[2, 8, 11, 13],[3, 5, 10, 16],[4, 6, 9, 15]]↵
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[[1, 8, 10, 15],[2, 7, 9, 16],[3, 6, 12, 13],[4, 5, 11, 14]]↵
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Can you give me an idea? thank you!↵
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