[dmurray]

Think of a number between 1 and 10. Multiply it by 9. Add the digits of that number. Subtract 5. Convert it to a letter using A = 1, B = 2, ...). Think of a country beginning with that letter. Take the second letter of the country. Think of an animal beginning with the new letter.

I predict you thought of (rot13) Ryrcunag.

Not exactly the same trick, and not guaranteed to work, but this one impressed me at a young age.

[cheerlessbog]

It works because there are remarkably few country names starting with D that don't start with DE. And everyone picks the same E.

Now try asking for an animal whose name starts with U.