Construct Matrix with given Permanent
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01-03-2024, 06:06 PM
Post: #2
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RE: Construct Matrix with given Permanent
(01-03-2024 05:53 PM)Albert Chan Wrote: To solve puzzle, we undo randomization, to make above "standard form". VA Square Matrix Permanent Puzzle VA Solution posted yesterday, so this is not a spoiler anymore. > m := [ [1,0,1,1,1,0,1,1,1,1,1,1], [0,0,1,1,0,0,0,0,0,1,0,1], [1,0,1,1,0,0,0,1,0,1,1,1], [0,0,1,0,0,0,0,0,0,1,0,0], [1,0,1,1,1,1,1,1,1,1,1,1], [0,0,1,1,0,0,0,0,0,1,1,1], [1,0,1,1,1,0,0,1,0,1,1,1], [0,1,0,1,1,1,1,1,1,1,0,1], [1,0,1,1,0,0,0,0,0,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1], [0,0,1,0,0,0,0,0,0,1,0,1], [1,0,1,1,1,0,1,1,0,1,1,1]] > s:=map(sum,m) → [10,4,7,2,11,5,8,9,6,12,3,9] If Permanent Puzzle setup as I predicted, "first row" has 9 1's We make them slightly different for sorting purpose. > s[0]:=9.5 > m:=map(sort(s), k->m[index(s,k)]) \(\left(\begin{array}{cccccccccccc} 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \end{array}\right)\) > SWAPCOL(m,10,12) > SWAPCOL(m,3,11) > SWAPCOL(m,4,9) > SWAPCOL(m,3,8) > SWAPCOL(m,1,7) > SWAPCOL(m,3,6) > SWAPCOL(m,1,4) > SWAPCOL(m,1,3) > SWAPCOL(m,1,2) \(\left(\begin{array}{cccccccccccc} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \end{array}\right) \) "First row" bits (if we move 8th row to top) for Permanent > 0b11111100110 + 1 2023 |
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Messages In This Thread |
Construct Matrix with given Permanent - Albert Chan - 01-03-2024, 05:53 PM
RE: Construct Matrix with given Permanent - Albert Chan - 01-03-2024 06:06 PM
RE: Construct Matrix with given Permanent - Maximilian Hohmann - 01-03-2024, 06:17 PM
RE: Construct Matrix with given Permanent - Albert Chan - 01-03-2024, 11:55 PM
RE: Construct Matrix with given Permanent - Albert Chan - 01-05-2024, 09:19 PM
RE: Construct Matrix with given Permanent - Albert Chan - 01-07-2024, 04:09 PM
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