superprismatic Posted October 19, 2010 Report Share Posted October 19, 2010 Here's a square matrix 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 matrix 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 the permutation which, when applied to both the rows and columns of the following matrix, will convert it into one which has constant diagonals: 11111111112222222 12345678901234567890123456 1 AZSJKCPTYQFDRVBHXOEWNLMGUI 2 BATKLDQUZRGESWCIYPFXOMNHVJ 3 IHARSKXBGYNLZDJPFWMEVTUOCQ 4 RQJABTGKPHWUIMSYOFVNECDXLZ 5 QPIZASFJOGVTHLRXNEUMDBCWKY 6 YXQHIANRWODBPTZFVMCULJKESG 7 LKDUVNAEJBQOCGMSIZPHYWXRFT 8 HGZQRJWAFXMKYCIOEVLDUSTNBP 9 CBULMERVASHFTXDJZQGYPNOIWK 10 KJCTUMZDIAPNBFLRHYOGXVWQES 11 VUNEFXKOTLAYMQWCSJZRIGHBPD 12 XWPGHZMQVNCAOSYEULBTKIJDRF 13 JIBSTLYCHZOMAEKQGXNFWUVPDR 14 FEXOPHUYDVKIWAGMCTJBSQRLZN 15 ZYRIJBOSXPECQUAGWNDVMKLFTH 16 TSLCDVIMRJYWKOUAQHXPGEFZNB 17 DCVMNFSWBTIGUYEKARHZQOPJXL 18 MLEVWOBFKCRPDHNTJAQIZXYSGU 19 WVOFGYLPUMBZNRXDTKASJHICQE 20 EDWNOGTXCUJHVZFLBSIARPQKYM 21 NMFWXPCGLDSQEIOUKBRJAYZTHV 22 POHYZREINFUSGKQWMDTLCABVJX 23 ONGXYQDHMETRFJPVLCSKBZAUIW 24 UTMDEWJNSKZXLPVBRIYQHFGAOC 25 GFYPQIVZEWLJXBHNDUKCTRSMAO 26 SRKBCUHLQIXVJNTZPGWOFDEYMA [/code] In other words, after the permutation is applied, the matrix becomes: [code] ABCDEFGHIJKLMNOPQRSTUVWXYZ ZABCDEFGHIJKLMNOPQRSTUVWXY YZABCDEFGHIJKLMNOPQRSTUVWX XYZABCDEFGHIJKLMNOPQRSTUVW WXYZABCDEFGHIJKLMNOPQRSTUV VWXYZABCDEFGHIJKLMNOPQRSTU UVWXYZABCDEFGHIJKLMNOPQRST TUVWXYZABCDEFGHIJKLMNOPQRS STUVWXYZABCDEFGHIJKLMNOPQR RSTUVWXYZABCDEFGHIJKLMNOPQ QRSTUVWXYZABCDEFGHIJKLMNOP PQRSTUVWXYZABCDEFGHIJKLMNO OPQRSTUVWXYZABCDEFGHIJKLMN NOPQRSTUVWXYZABCDEFGHIJKLM MNOPQRSTUVWXYZABCDEFGHIJKL LMNOPQRSTUVWXYZABCDEFGHIJK KLMNOPQRSTUVWXYZABCDEFGHIJ JKLMNOPQRSTUVWXYZABCDEFGHI IJKLMNOPQRSTUVWXYZABCDEFGH HIJKLMNOPQRSTUVWXYZABCDEFG GHIJKLMNOPQRSTUVWXYZABCDEF FGHIJKLMNOPQRSTUVWXYZABCDE EFGHIJKLMNOPQRSTUVWXYZABCD DEFGHIJKLMNOPQRSTUVWXYZABC CDEFGHIJKLMNOPQRSTUVWXYZAB BCDEFGHIJKLMNOPQRSTUVWXYZA Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 20, 2010 Report Share Posted October 20, 2010 16 26 4 5 22 23 21 18 7 10 13 3 8 25 14 20 17 9 2 1 15 6 12 19 11 24 Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted October 21, 2010 Author Report Share Posted October 21, 2010 16 26 4 5 22 23 21 18 7 10 13 3 8 25 14 20 17 9 2 1 15 6 12 19 11 24 Correct. Nice Going! I'll be posting a much more difficult related problem soon. I hope you try it. Quote Link to comment Share on other sites More sharing options...
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superprismatic
Here's a square matrix of letters with the
rows and columns numbered:
Find the permutation which, when applied to both the rows and columns of the following matrix, will convert it into one which has constant diagonals:Link to comment
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