I want to take each element in an array and do something to it with each other element of the same array. [...] what is this called?

Permutations (if ordered) or combinations (if unordered). The latter in this case.

For choosing two from the list, one could simply use:

for my $y (0..$#list) {
   for my $x ($y+1..$#list) {
      ...
   }
}
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But that would be inefficient here. It's O(N**2), whereas the following is O(N):

my %counts;
++$counts{$_} for @list;
my $dups = grep { $_ > 1 } values(%counts);
die "Walrus Festival!" if $dups >= 3;
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One can optimise the above to exit as soon as the answer is obvious:

my %counts;
my $dups;
for (@list) { 
   if (++$counts{$_} == 2) {
      if (++$dups >= 3) {
         die "Walrus Festival!";
      }
   }
}
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