The first method I ever used for this was an alternating hash.

my ($class, %flip_class) = qw(odd odd even even odd);

while (...) {
    $class = $flip_class{$class};
    ...
}
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or using a slightly obfuscated definition. It even saves 2 characters! :)

my ($class, %flip_class) = qw(odd even)[0,1,0,0,1];

while (...) {
    $class = $flip_class{$class};
    ...
}
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Another way I just thought of would be to use grep.

my $class = 'odd';

while (...) {
    ($class) = grep {!/$class/} qw(odd even);
    ...
}
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Personally, I'd probably stick with a bitwise xor ^, but any of these monastery solutions would work just fine.

- Miller