May be I have misunderstood the question,

I have made some variations in ur code. Instead of using hashes i have used arrays.

@numbers=(1,2,3,4);
@signs=('+','-','*','+');
@thirdarray=(2,3);

my @new = map { [$numbers[$_],$signs[$_]]} 0 .. $#numbers;


foreach my $i (0..$#new)
{
print $new[$i+1]->[0],$new[$i+1]->[1]."\n" if (grep{/^$new[$i]->[0]$/}
+@thirdarray);
}
[download]

Cheers.