Re: Better algorithm for Number Place Puzzle

Just a guess. Perhaps you could use the other monk's blanked out solution to create an initial grid. Then, recreate this solution in the other grids, but transform it in some simple way in order to make sure it doesn't break the rules. My shot - just a first guess - is below, hidden:

Hmm. Let's try a 2 x 2 version. The initial grid is

12
34
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obviously. Now you need to fill in

12--
34--
----
----
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Clearly, as you move across, you need to shift rows:

1234
3412
----
----
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And as you move down, you need to shift columns:

1234
3412
21--
43--
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note that the lower left grid is just the upper left grid with columns shifted along. Finally,

1234
3412
2143
4321
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it turns out that the column shift from the grid above, and the row shift from the grid to the left, give identical results.

Perhaps this will work with N>2. Or not. Enjoy.

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Comment on Re: Better algorithm for Number Place Puzzle Select or Download Code

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Re: Re: Better algorithm for Number Place Puzzle by blokhead (Monsignor) on May 23, 2004 at 23:27 UTC
This can be extended to create a random solution, just randomize the initial block. (This is similar to Abigail-II's solution). Here `@start` is a N by N matrix whose entries are a random permutation of {1, .., N^2}. `my $n = shift \|\| 3; my @start = do { use List::Util 'shuffle'; my @perm = shuffle 1 .. $n$n; map { my $row = $_; [ map { $perm[$row $n + $_] } 0 .. $n-1 ] } 0 .. $n-1; }; my @solution; for my $x ( 0 .. $n$n - 1 ) { for my $y ( 0 .. $n$n - 1 ) { my $block_x = int ($x / $n); my $block_y = int ($y / $n); $solution[$x][$y] = $start[ ($block_x + $y) % $n ][ ($block_y + $x) % $n ]; } } print join "" => map { "@$_\n" } @solution;` [download] blokhead	[reply] [d/l]

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Re: Re: Better algorithm for Number Place Puzzle
by blokhead (Monsignor) on May 23, 2004 at 23:27 UTC

Abigail-II

@start

my $n     = shift || 3;

my @start = do {
    use List::Util 'shuffle';
    my @perm = shuffle 1 .. $n*$n;

    map {
         my $row = $_;
         [ map { $perm[$row * $n + $_] } 0 .. $n-1 ]
    } 0 .. $n-1;
};

my @solution;

for my $x ( 0 .. $n*$n - 1 ) {
    for my $y ( 0 .. $n*$n - 1 ) {

        my $block_x = int ($x / $n);
        my $block_y = int ($y / $n);

        $solution[$x][$y] =
            $start[ ($block_x + $y) % $n ][ ($block_y + $x) % $n ];
    }
}

print join "" => map { "@$_\n" } @solution;
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blokhead

[reply]
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