Ok, I ran out of time working on the "brute force" checking, but here is the shell of a program which should reduce the number of numbers which need to be checked to a small enough set. Sorry I could not complete the program (as it was actually starting to be fun. *Smiles*)
in reply to Matrix Formation
use constant MATRIX_DIM => 3; # Set your matrix size here
use constant MAX_NUM => (10 ** MATRIX_DIM) - 1;
# Since you need to find 2 times the matrix width distinct numbers, yo
# have a divisor greater than the maximum number divided by that produ
# For example, a 3 x 3 matrix has a maximum number of 999. You need 6
# numbers to "solve" the matrix, so the maximum possible divisor would
+ be 166.
# 166 would result in 166, 332, 498, 664, 830, and 996.
my $Divisor = int(MAX_NUM / (MATRIX_DIM * 2));
# INCOMPLETE CODE
# Place code here which checks every combination of MATRIX_DIM numbe
+rs as rows
# and sees if there are MATRIX_DIM other numbers which can act as co
# For example, for a 3 x 3 matrix, this code should go through each
# of three number (for rows) from the passed array and see if there
# other numbers which would work with the selected rows as columns.
# be a workable computation for all smaller matrix sizes.
while ($Divisor >= 1)
foreach (1..int(MAX_NUM / $Divisor))
next if (($Divisor * $_) < (MAX_NUM / 10)); #Skip numbers which be
+gin with zero
push @Num, ($Divisor * $_);
print 'Checking solution for divisor ',$Divisor,': ',join('-',@Num),
last if ($#Sol > -1);
if ($#Sol > -1)
print 'Maximum divisor is ',$Divisor,', solution is ',join('-',@Sol)
print 'No solution found...',"\n";
Update: I finished code which will work on any size matrix and posted it Here.
Please note: I use "work" in the loosest terms as solving the 4x4 took 1.5 hours on my notebook.