Looking for a good pub quiz question? This one might catch some people out. Europe has a surprising number of monarchies, ranging from the well known to the obscure. They cover the spectrum from constitutional monarch through power sharing to absolute ruler. The youngest monarchy was instituted in 1929 (and that's a clue).
Christina of Sweden was five when her father King Gustav II Adolf fell in the battle of Lützen. Upon his death, her mother Queen Maria Eleonora was put under house arrest and exiled to castle Gripshom. On the express wish of the king, Christina was raised and trained as a prince and not a princess. At 16, she declined to co-rule with a regency council; instead she took full control at 18 when coming of age.
There are Princes and Princesses, and then there are Princes and Princesses. Some are Royal or more, some are not. The problem lies in geography. Depending on where the title came from, the title of Prince does not mean the same thing. The puzzle can be solved given some knowledge of geography and history, and quite some of the muddle derived from translating foreign titles into English.