superprismatic Posted October 21, 2010 Report Share Posted October 21, 2010 Here's a square array of letters with the rows and columns numbered: 123456789 1 AGDICBHFE 2 DAGCFEBIH 3 GDAFIHECB 4 BHEADCIGF 5 HEBGAIFDC 6 IFCHBAGED 7 CIFBEDAHG 8 EBHDGFCAI 9 FCIEHGDBA [/code] We can reorder the rows and columns with the same permutation to convert the above array into one with constant diagonals: [code] 398274165 3 ABCDEFGHI 9 IABCDEFGH 8 HIABCDEFG 2 GHIABCDEF 7 FGHIABCDE 4 EFGHIABCD 1 DEFGHIABC 6 CDEFGHIAB 5 BCDEFGHIA Find a permutation which, when applied to both the rows and columns of the binary array 11111111112222222 12345678901234567890123456 1 10010111010010000101100111 2 00011100101001101001100111 3 00101011000101110011110001 4 10011010100100110010111001 5 01110011110001011000010110 6 00010101100111101011001001 7 00110101110110111010000001 8 01011001010111000010111100 9 10011111100001000111001010 10 11011001101000000100101111 11 10101001101010000110011011 12 11001100010101101110000110 13 11101110100010010101110000 14 00100110110011110101001010 15 11001011011010100001011001 16 11010110111000011001010100 17 00000111011011111100010100 18 01100111000101010010001111 19 11101000001110001100110110 20 01000000111101001111110100 21 11100010010110110010100110 22 01101000001110101101101010 23 00010100011100110111001011 24 01110010101000101010111001 25 10111101001001011001010100 26 10100000011111011100101001 [/code] will convert it into [code] 10001010011010111101000101 11010100101111000110100001 10001111000110111000000111 10110110011001101011000100 11101000101001101000111100 11100100010101100000111110 01101001010111011101001000 10101100011110110101000010 11001001110000000111111001 00000010010111111110110001 01011001011001010011000111 10010101110100001011001101 10010000000110110111001111 10010111001001010000111101 00110111110011000110101000 01001110100011101100011100 00101001111100001011010110 01110101101000101110010010 11000111100100010001110110 01011000110110001001111010 00100011001110010011111001 00110111001011110110100000 01110010111000100100001111 11011100000010001001111011 00111010100101110000110011 01101011101001011110000010 Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted October 22, 2010 Report Share Posted October 22, 2010 (edited) Nice puzzle 16 26 5 13 4 3 2 25 23 20 1 14 17 21 22 24 9 11 18 6 12 19 15 7 8 10 Edited October 22, 2010 by bushindo Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 23, 2010 Author Report Share Posted October 23, 2010 Nice puzzle 16 26 5 13 4 3 2 25 23 20 1 14 17 21 22 24 9 11 18 6 12 19 15 7 8 10 Great, that's right! Now I've got a similar puzzle in 4 dimensions. Take a gander! Quote Link to comment Share on other sites More sharing options...
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superprismatic
Here's a square array of letters with the
rows and columns numbered:
Find a permutation which, when applied to both the rows and columns of the binary arrayLink to comment
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