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my $number_of_true_variables = grep { $_ } $x, $y, $z;

if ( $number_of_true_variables == 1 ) {
    print "Exactly one variable set\n";
}

sub number_of_true_variables {
    return scalar grep { $_ } @_;
...
if ( number_of_true_variables( $x, $y, $z ) == 1 ) {
    print "Exactly one variable set\n";
}

sub exactly_one_is_set {
    my $number_of_true_variables = grep { $_ } @_;
...
if ( exactly_one_is_set( $x, $y, $z ) ) {
    print "Exactly one variable set\n";
}