It is the year 10,000,000,000, and materalisation has been invented. At the same time, Nintendo has materialised every single Pokémon (countably infinitely many now!) to fight against finitely many lions (neither the Pokémon nor the lions are hostile to any other species). You don't know exactly how many lions there are, only that it is a finite number (it could even be 0).
It is now the break before the fight. All the lions and Pokémon are standing in a line, but you have no way of telling who are the lions and who are the Pokémon.
You can ask anyone in the line a boolean combination of these questions:
- Are you a lion?
- Is the n-th in line from the left a lion?
The Pokémon and lions all know the identites of everyone in the line (first one on the left). All Pokémon tell the truth and only the truth, while all lions say yes or no randomly.
It will take you an infinitesimal amount of time to ask a question, so you can ask as many questions as you want (finitely or infinitely many) before the fight starts.
Question: How can you identify one Pokémon, asking the fewest questions possible?
(If infinitely many questions are asked, they are counted by order type, Asking positions from the left [1, 1, 2, 2, 3, 3...] would be $\omega$ questions, but asking [1, 2, 3, ..., 1, 2, 3, ...] would be $\omega \times 2$ questions)