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$x = 0;
$y = 1;
$z = 0;

$x = 5;
$y = undef;
$z = 5;

my $count = 0;
$x && $count++;
...
if($count == 1) {
    print "Exactly one variable set\n";
}

if((grep { $_ } $x, $y, $z) == 1) {
    print "Exactly one variable set\n";
}