Thank you for your thorough feedback. I was sure I'd replied to your message back when it was fresh, so I apologise it didn't send. I'll need to take a look at Oracle of Seasons.
One of the main issues of the demo is that it isn't clear when a number is being used up, or what the generator is used for. This leads to people assuming random numbers.
When I revisit this concept I'll start with a much smaller area to ensure the idea gets thoroughly ingrained in the player's mind. Then I'll cement the rules of interacting with the RNG. The methods for interaction will change between towns.
The champion's number is based on the number sequence, but depending on where you are in that sequence means they'll ask for a different initial number - this is to ensure the player doesn't get the correct answer immediately by chance.
Felix is just wordplay on felis/felicity (luck).