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### Magic Birthday Square

by YuckFoo (Abbot)
 on May 03, 2002 at 18:28 UTC ( #163864=CUFP: print w/replies, xml ) Need Help??

Here's a little ditty to put your birthday in the corners of a 4 x 4 magic square. In a magic square, the sum of all columns, all rows, and the two major diagonals is the same.

The squares made with this algorithm also have same values in the corner 2 x 2 squares, and the center 2 x 2 square.

The square has the maximum number of unique values allowed by the algorithm. I didn't devise a clever way to disallow negative numbers so folks with low birthmonth or birthday might see negative values. There is a random factor, so running the program again might generate an all positive square.

SquareFoo

```
#!/usr/bin/perl

use strict;

if (@ARGV < 1) {
print STDERR "\nUsage: \$0 mmddyyyy\n\n"; exit;
}

my (\$mm, \$dd, \$cc, \$yy) = (\$ARGV[0] =~ m{(..)}g);

my \$ms = [];

\$ms->[0] = [\$mm, \$cc, \$yy, \$dd];
\$ms->[1] = [\$yy, \$dd, \$mm, \$cc];
\$ms->[2] = [\$dd, \$yy, \$cc, \$mm];
\$ms->[3] = [\$cc, \$mm, \$dd, \$yy];

my \$most = 12 + uniq(\$ms);

if (\$mm == \$dd) { \$most--; }
if (\$mm == \$cc) { \$most--; }
if (\$yy == \$dd) { \$most--; }
if (\$yy == \$cc) { \$most--; }

while (uniq(\$ms) < \$most) {
if (int(rand(2))) {
if (int(rand(2))) {
rot (\$ms, 1, 0,  1);
rot (\$ms, 1, 2, -1);
}
else {
rot (\$ms, 1, 0, -1);
rot (\$ms, 1, 2,  1);
}
}
else {
if (int(rand(2))) {
rot (\$ms, 0, 1,  1);
rot (\$ms, 2, 1, -1);
}
else {
rot (\$ms, 0, 1, -1);
rot (\$ms, 2, 1,  1);
}
}
}

show (\$ms);

#-----------------------------------------------------------
sub uniq {

my (\$ms) = @_;
my (%used);

for my \$row (0..3) {
for my \$col (0..3) {
\$used{\$ms->[\$row][\$col]}++;
}
}

return scalar(keys(%used));
}

#-----------------------------------------------------------
sub rot {

my (\$ms, \$row, \$col, \$val) = @_;

\$ms->[\$row]  [\$col]   += \$val;
\$ms->[\$row+1][\$col+1] += \$val;
\$ms->[\$row]  [\$col+1] -= \$val;
\$ms->[\$row+1][\$col]   -= \$val;
}

#-----------------------------------------------------------
sub show {

my (\$ms) = @_;

for my \$row (0..3) {
for my \$col (0..3) {
printf(STDOUT "%2d ", \$ms->[\$row][\$col]);
}
print STDOUT "\n";
}
}

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