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my $count = 0;
$_ and $count++ for ($x,$y,$z);
if (1 == $count) {
  print "Exactly one variable set\n";
}

if (1 == do {my $cnt=0; $_ and $cnt++ for ($x,$y,$z); $cnt } {
  print "Exactly one variable set\n";
}

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