What's the best way of testing if exactly one out of three variables are set?

There's three variables $x, $y, and $z. If there's exactly one true value, as in 

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

[download]
the test should succeed. But if there's more (or less) than one true value, as in 
$x = 5;
$y = undef;
$z = 5;

[download]
then I'd like the test to fail.

Here's a clunky solution: 

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

[download]
Here's a more elegant one: 
if((grep { $_ } $x, $y, $z) == 1) {
    print "Exactly one variable set\n";
}

[download]
But none of them is really intuitive. Is there a better way?

In reply to One out of three ain't bad by saintmike

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.