Dear Monks
I found an interesting puzzle and here is my attempt to solve it. Let say we have NxN matrix.
[
[1, 2]
[4, 8]
]
By Joining the columns and rows individually, I get the following four formednumbers.
12,14,28,48 There Common Divisor is '2'. I like to find the matrix with the highest common divisor. Some condtions are..
 No formednumber should start with 0.
 No two formednumbers be same.
I can do it easily for 2x2 matrix and found highest divisor as 7.
and the formednumbers : 28,21,14,84.
[[2,8]
[1,4]]
How I can do with higher dimentions more efficiently?
Even for 3X3 with it has to test around billion numbers with my method.
$ += 1;
foreach my $divider (2..9){
print "Divider $divider\n";
N: foreach $n (1111..9999){
next if $n =~ /0\d+/;
@n = split //,$n;
my $count = 0;
my @pairs;
my %pairs;
foreach (qw(01 02 13 23)){
my($p,$q) = split //;
my $num = $n[$p].$n[$q];
push @pairs, $num;
next N if defined $pairs{$num};
$pairs{$num} = 1;
$count++ if $num % $divider == 0;
}
print join " " => @pairs,"\n" if $count == 4;
}
}
Thanks
artist
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