Here's an initial puzzle:
All plods are also plops.
Half the plops are also ploms.
Half the plods are also ploms.
Half the plops are also plods.
There are twice as many plops as either ploms or plods.
There are two plods that are also plops.
How many pure plops are there?
I have to agree with Bulldog. How can there be more than one pure plop? But I counted a few props, proms, and prods that did not make it into the accounting.