SudokuSolver Forum

Sterling work Richard.
An exercise in recursive programming. Shame I can't participate in this at present.

_________________
I have 81 brain cells left, I think.

Glyn, you need to brush up on your programming and I definitely need to brush up an my math. Back at the university (in another lifetime) I studied quite a bit of math (Calculus-1, Calculus-2, Imaginary-Calculus, Algebra-1, Statistical-Analysis. Numerical Methods and State-Machines). Except for Numerical Methods and State-Machines, which I use now and then I am ashamed to say that I due to lack of practice have forgotten everything else.

_________________
Quis custodiet ipsos custodes?

Normal: [D  Y-m-d,  G:i]     PM->email: [D, d M Y H:i:s]

Although not strictly required, recursion is quite efficient in this case.

I'm not convinced we're heading for a unique solution on this one.

[Edit] Here's the consolidated view up to 5 Rods - need to do a cross-check on 5 to make sure. 6 Rods solution is proving elusive at the moment, so don't know if I'll get a solution before I go away on vacation tonight.

{1}

{1, 3} {2}
{1, 2} {4}

{2, 1, 7} {4, 5} {6}
{3, 1, 5} {2, 8} {7}
{1, 3, 6} {2, 5} {8}
{1, 2, 5} {4, 6} {9}
{3, 2, 4} {1, 7} {10}

{2, 1, 12, 4} {6, 5, 9} {8, 10} {7}
{2, 13, 1, 4} {7, 3, 9} {6, 11} {8}
{1, 11, 2, 4} {3, 7, 9} {5, 15} {8}
{1, 4, 11, 2} {7, 3, 9} {6, 14} {8}
{2, 11, 1, 5} {3, 7, 8} {4, 16} {9}
{2, 1, 10, 6} {5, 7, 8} {4, 14} {9}
{1, 13, 2, 4} {7, 3, 8} {5, 12} {9}
{1, 11, 3, 5} {4, 6, 7} {2, 16} {9}
{1, 13, 2, 3} {6, 4, 7} {8, 12} {9}
{2, 3, 11, 4} {6, 1, 12} {8, 9} {10}
{2, 7, 8, 3} {5, 1, 13} {4, 12} {10}
{2, 13, 1, 4} {6, 3, 8} {7, 12} {10}
{1, 11, 5, 3} {2, 7, 6} {4, 14} {10}
{1, 13, 2, 4} {5, 3, 9} {7, 11} {10}
{1, 6, 9, 4} {3, 2, 12} {8, 10} {11}
{2, 3, 11, 4} {7, 1, 9} {6, 13} {12}
{2, 6, 3, 7} {1, 14, 5} {4, 13} {12}
{1, 10, 6, 3} {2, 5, 8} {4, 14} {12}
{1, 8, 6, 5} {4, 3, 10} {2, 16} {12}
{1, 3, 11, 5} {7, 2, 8} {6, 12} {13}
{1, 6, 2, 10} {4, 11, 5} {3, 14} {13}
{1, 12, 4, 2} {5, 3, 7} {9, 11} {14}
{1, 11, 6, 2} {3, 4, 9} {5, 10} {14}
{4, 6, 2, 5} {1, 15, 3} {9, 11} {14}
{1, 7, 10, 2} {4, 5, 6} {3, 13} {14}
{1, 9, 2, 6} {4, 3, 13} {5, 14} {15}
{1, 2, 11, 6} {4, 5, 7} {8, 10} {15}
{3, 11, 2, 4} {1, 8, 10} {5, 7} {15}
{1, 9, 3, 4} {5, 6, 8} {2, 18} {15}
{2, 8, 4, 3} {1, 5, 13} {9, 11} {16}
{3, 8, 2, 7} {4, 1, 14} {6, 12} {16}
{2, 4, 11, 3} {1, 7, 5} {9, 10} {16}
{1, 3, 8, 6} {5, 2, 13} {9, 10} {16}
{2, 6, 1, 11} {4, 10, 5} {3, 13}{17}
{7, 2, 3, 8} {1, 14, 4} {6, 10} {17}
{3, 2, 9, 4} {1, 7, 12} {6, 10} {17}
{1, 11, 5, 3} {2, 7, 6} {4, 10} {18}
{4, 9, 1, 6} {2, 3, 12} {8, 11} {18}
{1, 4, 8, 3} {2, 7, 10} {6, 14} {18}
{1, 2, 10, 5} {4, 7, 9} {6, 8} {19}
{1, 9, 4, 2} {3, 5, 12} {7, 11} {19}
{5, 6, 1, 8} {3, 10, 4} {2, 16} {19}
{5, 3, 4, 6} {1, 14, 2} {9, 11} {19}
{3, 2, 9, 4} {1, 6, 10} {8, 12} {19}
{1, 5, 7, 3} {2, 9, 8} {4, 14} {20}
{4, 5, 2, 8} {1, 13, 3} {6, 12} {20}
{1, 4, 11, 2} {7, 3, 9} {6, 8} {20}

{2, 7, 15, 3, 8} {1, 16, 4, 10} {5, 23, 6} {13, 19} {12}
{3, 8, 15, 2, 7} {1, 19, 10, 4} {5, 16, 6} {13, 18} {12}
{3, 11, 4, 12, 5} {6, 19, 1, 8} {2, 22, 7} {10, 23} {13}
{1, 11, 10, 8, 5} {2, 4, 20, 7} {3, 16, 9} {15, 17} {14}
{4, 2, 12, 10, 7} {1, 20, 5, 8} {3, 16, 11} {9, 23} {15}
{2, 12, 8, 10, 3} {5, 4, 19, 6} {1, 15, 11} {7, 24} {17}
{3, 1, 15, 8, 6} {2, 11, 9, 12} {7, 18, 10} {5, 26} {17}
{3, 8, 2, 18, 4} {1, 14, 12, 7} {5, 16, 9} {6, 23} {17}
{2, 3, 16, 8, 4} {1, 14, 11, 9} {7, 6, 17} {10, 22} {18}
{3, 12, 7, 2, 11} {1, 16, 10, 4} {5, 23, 6} {8, 25} {18}
{3, 17, 7, 1, 5} {4, 12, 10, 9} {2, 21, 11} {14, 15} {18}
{3, 5, 16, 1, 9} {2, 13, 14, 6} {7, 12, 11} {4, 28} {18}
{2, 6, 18, 4, 3} {1, 11, 9, 14} {5, 10, 17} {13, 16} {19}
{2, 10, 6, 8, 9} {4, 3, 22, 5} {1, 20, 11} {13, 15} {19}
{7, 6, 12, 2, 8} {3, 21, 5, 4} {1, 16, 15} {11, 23} {19}
{3, 5, 16, 1, 9} {2, 13, 14, 6} {7, 11, 12} {4, 28} {19}
{2, 12, 10, 5, 6} {4, 3, 16, 9} {1, 17, 13} {8, 26} {20}
{3, 4, 17, 6, 5} {8, 1, 13, 12} {2, 16, 15} {10, 19} {20}
{7, 1, 14, 3, 9} {5, 11, 13, 6} {2, 21, 10} {4, 28} {20}
{3, 13, 5, 10, 4} {1, 24, 2, 7} {6, 11, 12} {8, 22} {20}
{1, 7, 14, 9, 3} {6, 13, 5, 11} {2, 15, 10} {4, 28} {20}
{1, 6, 17, 5, 4} {8, 2, 11, 14} {3, 16, 15} {12, 18} {20}
{3, 14, 5, 7, 6} {1, 8, 15, 10} {4, 16, 11} {2, 28} {21}
{2, 8, 6, 11, 7} {4, 19, 3, 9} {5, 15, 13} {1, 29} {21}
{1, 18, 5, 4, 7} {3, 10, 12, 8} {2, 15, 14} {6, 26} {21}
{1, 11, 8, 5, 9} {2, 4, 23, 3} {7, 10, 18} {15, 16} {21}
{2, 8, 12, 4, 7} {3, 14, 13, 5} {9, 6, 19} {1, 28} {21}
{2, 3, 19, 6, 4} {8, 1, 14, 12} {11, 7, 13} {16, 17} {21}
{3, 9, 6, 10, 4} {5, 17, 2, 11} {1, 26, 7} {8, 23} {21}
{2, 9, 17, 1, 4} {3, 7, 13, 12} {6, 8, 16} {15, 19} {21}
{1, 12, 16, 2, 4} {5, 3, 17, 7} {10, 9, 14} {11, 15} {21}
{1, 8, 18, 2, 4} {5, 7, 10, 13} {3, 16, 15} {11, 14} {21}
{3, 4, 15, 8, 5} {2, 12, 6, 11} {1, 24, 9} {10, 16} {21}
{1, 10, 7, 14, 2} {5, 4, 20, 6} {3, 12, 13} {8, 19} {22}
{2, 18, 1, 9, 5} {3, 8, 16, 7} {4, 13, 12} {6, 26} {22}
{3, 6, 19, 2, 5} {4, 13, 1, 15} {8, 12, 11} {10, 24} {22}
{1, 3, 8, 13, 6} {2, 16, 10, 7} {5, 15, 14} {9, 23} {22}
{1, 10, 14, 5, 2} {8, 15, 3, 9} {13, 4, 16} {6, 28} {22}
{6, 3, 15, 1, 10} {2, 5, 23, 4} {12, 8, 13} {14, 17} {22}
{1, 9, 11, 7, 6} {4, 12, 14, 5} {2, 15, 8} {3, 29} {22}
{3, 5, 20, 1, 6} {10, 9, 4, 11} {2, 14, 17} {12, 18} {22}
{1, 9, 17, 2, 3} {8, 7, 6, 12} {4, 16, 14} {11, 24} {23}
{3, 5, 16, 1, 9} {2, 13, 14, 6} {11, 7, 12} {4, 28} {23}
{4, 2, 8, 16, 5} {7, 15, 3, 9} {1, 19, 13} {11, 17} {23}
{1, 12, 6, 11, 4} {3, 5, 20, 7} {2, 14, 10} {9, 22} {23}
{4, 14, 2, 10, 5} {1, 24, 3, 6} {11, 8, 13} {7, 22} {23}
{1, 8, 2, 14, 5} {3, 15, 13, 4} {6, 20, 7} {12, 22} {23}
{3, 5, 14, 6, 7} {1, 17, 12, 4} {2, 9, 15} {10, 21} {23}
{3, 11, 8, 2, 7} {4, 12, 13, 5} {1, 26, 6} {15, 20} {23}
{1, 7, 12, 3, 10} {4, 17, 9, 5} {2, 16, 11} {6, 28} {24}
{2, 9, 17, 1, 5} {3, 10, 12, 8} {4, 15, 16} {7, 14} {24}
{5, 1, 16, 3, 9} {4, 10, 13, 8} {7, 11, 15} {2, 30} {24}
{2, 3, 18, 8, 4} {7, 6, 9, 10} {1, 16, 11} {14, 20} {24}
{2, 10, 17, 1, 3} {8, 6, 5, 15} {7, 16, 9} {13, 22} {24}
{2, 15, 11, 1, 6} {4, 16, 5, 9} {10, 3, 19} {8, 23} {24}
{4, 11, 7, 2, 10} {1, 5, 23, 3} {8, 13, 14} {16, 17} {25}
{2, 4, 12, 14, 3} {10, 5, 8, 11} {1, 20, 7} {9, 22} {25}
{2, 5, 9, 13, 6} {3, 20, 1, 10} {4, 8, 18} {15, 17} {25}
{7, 5, 10, 4, 9} {2, 6, 21, 3} {1, 17, 16} {11, 20} {25}
{2, 5, 19, 3, 6} {8, 12, 1, 10} {4, 14, 16} {15, 17} {25}
{2, 14, 4, 8, 7} {3, 10, 11, 6} {1, 22, 9} {5, 29} {25}
{3, 1, 15, 8, 6} {2, 11, 9, 12} {7, 10, 18} {5, 26} {25}
{2, 11, 17, 1, 3} {8, 6, 10, 9} {5, 15, 7} {12, 23} {26}
{3, 4, 11, 12, 5} {2, 6, 16, 9} {13, 1, 20} {10, 19} {26}
{1, 6, 18, 4, 5} {8, 11, 2, 10} {3, 17, 15} {14, 16} {26}
{7, 3, 13, 4, 8} {1, 21, 9, 2} {5, 14, 15} {6, 18} {26}
{3, 11, 4, 12, 5} {1, 6, 13, 9} {2, 23, 8} {10, 24} {26}
{2, 5, 18, 6, 4} {12, 8, 1, 13} {3, 16, 11} {15, 17} {26}
{1, 18, 2, 9, 4} {5, 3, 14, 10} {7, 16, 12} {6, 25} {26}
{5, 12, 7, 3, 8} {2, 14, 9, 6} {1, 20, 13} {4, 28} {26}
{1, 5, 19, 3, 7} {9, 8, 4, 11} {2, 18, 13} {14, 16} {26}
{1, 8, 5, 17, 2} {6, 10, 11, 7} {12, 3, 20} {4, 25} {26}
{1, 7, 18, 4, 2} {5, 9, 3, 16} {11, 10, 13} {15, 20} {27}
{4, 9, 15, 1, 5} {2, 8, 12, 11} {3, 14, 18} {7, 19} {27}
{5, 4, 6, 13, 7} {1, 21, 3, 8} {2, 12, 17} {16, 18} {27}
{1, 5, 14, 12, 3} {2, 11, 10, 7} {8, 16, 9} {4, 18} {27}
{2, 13, 1, 8, 10} {3, 4, 21, 5} {6, 17, 12} {11, 20} {27}
{3, 7, 18, 1, 5} {9, 8, 4, 11} {2, 20, 13} {14, 16} {27}
{5, 15, 4, 2, 8} {3, 9, 16, 7} {1, 17, 13} {11, 22} {27}
{1, 7, 14, 2, 10} {3, 15, 13, 4} {5, 6, 19} {9, 20} {27}
{4, 6, 16, 2, 5} {1, 19, 12, 3} {9, 8, 13} {11, 14} {27}
{1, 12, 7, 11, 4} {3, 2, 21, 6} {8, 9, 16} {10, 14} {28}
{2, 1, 15, 7, 10} {5, 9, 12, 8} {6, 13, 11} {4, 27} {28}
{1, 9, 13, 7, 5} {6, 15, 3, 8} {14, 2, 17} {4, 27} {28}
{3, 1, 15, 8, 6} {2, 11, 9, 12} {10, 7, 18} {5, 26} {28}
{1, 10, 5, 17, 2} {3, 9, 14, 4} {7, 13, 8} {6, 25} {29}
{4, 1, 20, 3, 7} {6, 9, 2, 16} {8, 14, 12} {13, 19} {29}
{2, 12, 7, 6, 3} {1, 17, 5, 10} {4, 20, 11} {8, 26} {29}
{1, 9, 6, 17, 2} {3, 8, 13, 7} {4, 14, 12} {5, 22} {29}
{2, 4, 17, 1, 9} {3, 12, 13, 7} {11, 5, 14} {8, 26} {29}
{3, 8, 2, 18, 4} {1, 14, 12, 7} {5, 16, 9} {6, 17} {29}
{2, 4, 20, 1, 7} {10, 9, 3, 11} {5, 13, 17} {15, 16} {29}
{6, 9, 7, 4, 8} {3, 14, 13, 5} {2, 21, 10} {1, 24} {29}
{2, 12, 8, 10, 3} {1, 16, 7, 4} {9, 6, 19} {5, 26} {29}
{2, 6, 18, 4, 3} {11, 9, 1, 13} {5, 12, 15} {16, 19} {29}
{1, 4, 16, 7, 6} {3, 14, 8, 10} {2, 9, 15} {12, 19} {30}
{7, 2, 12, 3, 8} {1, 18, 10, 6} {4, 22, 5} {13, 20} {30}
{2, 14, 4, 9, 6} {1, 21, 3, 7} {5, 12, 11} {8, 26} {30}
{1, 15, 7, 2, 10} {5, 13, 8, 6} {3, 17, 11} {4, 29} {30}
{3, 5, 19, 1, 6} {4, 11, 2, 16} {12, 9, 14} {10, 22} {30}
{4, 1, 15, 6, 7} {3, 14, 10, 8} {9, 2, 23} {12, 19} {30}
{3, 7, 4, 13, 5} {6, 19, 1, 8} {2, 21, 12} {15, 16} {30}
{3, 7, 13, 8, 4} {2, 16, 6, 5} {1, 14, 19} {9, 17} {30}
{2, 11, 1, 16, 5} {7, 8, 10, 9} {3, 23, 6} {4, 20} {31}
{2, 12, 8, 10, 3} {5, 4, 19, 6} {1, 15, 11} {7, 17} {31}
{3, 6, 19, 1, 4} {12, 2, 8, 13} {7, 11, 16} {15, 17} {31}
{1, 15, 6, 4, 8} {5, 2, 17, 11} {3, 20, 9} {13, 14} {31}
{3, 17, 1, 6, 5} {2, 14, 9, 10} {4, 22, 8} {13, 15} {31}
{3, 6, 16, 2, 8} {1, 13, 15, 5} {7, 12, 11} {4, 17} {31}
{2, 7, 6, 14, 3} {1, 21, 4, 8} {11, 5, 19} {10, 18} {31}
{4, 5, 15, 3, 7} {2, 11, 8, 14} {1, 16, 12} {6, 26} {31}
{2, 14, 11, 1, 7} {5, 15, 3, 6} {4, 17, 13} {10, 22} {31}
{1, 15, 8, 4, 6} {2, 5, 14, 11} {3, 17, 9} {13, 22} {31}
{6, 2, 15, 1, 11} {3, 4, 21, 5} {10, 9, 13} {14, 20} {31}
{2, 16, 6, 1, 10} {5, 9, 12, 8} {4, 15, 13} {3, 27} {31}
{4, 8, 10, 7, 6} {3, 2, 19, 9} {1, 15, 11} {14, 20} {32}
{2, 3, 18, 4, 6} {9, 7, 8, 11} {1, 12, 17} {14, 20} {32}
{5, 10, 8, 1, 11} {2, 4, 22, 3} {7, 14, 13} {16, 17} {32}
{1, 14, 4, 7, 9} {3, 2, 22, 6} {8, 13, 10} {12, 17} {32}
{1, 10, 7, 12, 4} {3, 2, 20, 6} {8, 13, 14} {9, 15} {32}
{3, 10, 5, 12, 4} {6, 20, 2, 7} {8, 11, 14} {1, 23} {32}
{5, 2, 15, 3, 6} {1, 10, 19, 4} {8, 13, 14} {12, 16} {32}
{1, 5, 4, 17, 3} {2, 12, 11, 8} {7, 15, 13} {16, 18} {32}
{6, 8, 2, 11, 7} {4, 19, 3, 9} {1, 24, 5} {15, 17} {33}
{1, 14, 9, 4, 3} {6, 11, 8, 10} {2, 20, 12} {5, 21} {33}
{1, 2, 15, 8, 6} {4, 9, 11, 10} {7, 12, 16} {5, 22} {33}
{3, 11, 4, 12, 5} {6, 19, 1, 8} {2, 22, 7} {10, 13} {33}
{4, 2, 20, 1, 7} {10, 9, 5, 11} {3, 12, 17} {13, 18} {33}
{1, 8, 12, 4, 6} {2, 13, 14, 5} {7, 11, 17} {3, 23} {33}
{2, 7, 14, 8, 3} {1, 12, 5, 10} {4, 20, 6} {16, 19} {33}
{1, 10, 14, 5, 2} {8, 15, 3, 9} {13, 4, 16} {6, 22} {34}
{1, 2, 10, 11, 6} {4, 15, 7, 9} {5, 20, 8} {14, 18} {34}
{3, 8, 12, 2, 7} {6, 13, 5, 10} {1, 26, 4} {16, 17} {35}
{2, 9, 8, 10, 5} {3, 21, 1, 6} {4, 12, 14} {13, 20} {35}
{1, 3, 18, 7, 2} {10, 5, 8, 11} {6, 14, 12} {16, 17} {35}
{2, 14, 3, 9, 6} {1, 10, 13, 7} {4, 21, 8} {5, 22} {35}

Not converging then Richard 1,1,5,63 ..... I see that you are still on 1,3 in the outer loops doing the 5 rod case and 5 already.

Faites Vos Jeux, Mesdames Et Messieurs. How many 5 rod solutions?
My first guess 10,000.

_________________
I have 81 brain cells left, I think.

We may never know . . .

It'll take a while - meanwhile I'm trying to work out the 6 rods

By the way: should be 1, 2, 5, 63 . . .

I think my guess for 5 rods is a 'bit' high, there is some powerful cancelling going on between the rods.

On the plus side a multiplicity of solutions means you may find the first near the beginning of the outer loops hopefully near the first permitted value of 1,2,4 (3 excluded by 1,2). Of course if Matt is right and the solution is unique there will be a long wait.

_________________
I have 81 brain cells left, I think.

I found 136 Solutions for 5 Rods.

Great work Richard so now we have:-
1, 2, 5, 63,136
The explosive growth is being suppressed by the increase in constraints. Only up by a factor ~2 this time instead of ~12. Really amazing behaviour. If the constraints win the battle maybe the solution is unique.

_________________
I have 81 brain cells left, I think.

Not sure. Just double checking some of my results and looks like I mis-counted the 4 rod solutions. I can only count 47 this morning.

Just redoing the 5 rods to make sure I haven't gone completely bonkers.

Up to 15.8 Billion iterations so far and still not a single hit . . .