I'd like to count keys in a hash of hashes based on their values. I have an example hash snipit as follows: 
%hash = (
          'a' => {
                   'x' => 40,
                   'z' => 102
                 },
          'b' => {
                   'z' => 100,
                   'x' => 10,
                   'y' => 20
                 },
          'c' => {
                   'x' => 50
                 },
          'd' => {
                   'z' => 101,
                   'y' => 30
                 }
        );

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There are a couple of different ways I'd like to count the keys on this hash.

1. How can I count the number of keys where 'x' has a defined value, but does not have a value for 'y'?

2. How can I count the number of keys which have a defined value for 'z'?

Thanks for all shared wisdom.

Update:

Thanks for showing me how to do this.

One additional thing I forgot to ask in my original question.

How would I also count the number of keys with a value of 101 for 'z'?

In reply to Counting hash of hashes elements by albert

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