Breeding pets would be a pet related feature in prodigy.
Overview[]
The first time a player breeds a pet, Noot will walk them through it, but here is the course of events: To breed a pet, the player will select an icon with a blue and pink at the top of their pet book. All female pets will be sorted to the left, while all male pets will be sorted to the right. After you select one male and one female, a short animation will play, and Noot will say that he thinks the pets are affected by Shadow magic, but he doesn't know why (only during first time). The player will battle an entity similar to a shroud in Tower Town. Then they will have to answer 5-10 questions. The more questions answered correctly, the more the shroud will clear, and the higher chance of success. When the battle ends, the shroud will fade, and there will be a battle header. Instead of it saying "You Won!" It'll say "Breeding Fail..." or "Breeding Success!" to announce the outcome.
Afterwards, Noot will say "You got an item!" and then you'll be able to see how many and what type of eggs you received (Note that the eggs will not appear in you inventory, the same way runes don't appear in there). Noot will then say "Check your nest to see when they'll hatch!" The player will then navigate to their pet book and a small red exclamation point will hover over a nest icon next to the breeding icon. They'll be an artwork of a nest with eggs sitting inside, then below will be a scrollable list of the player's eggs. When the player clicks on one, it'll show a detailed image of the egg, a countdown to when it'll hatch, and the type of egg (a question mark will appear if the player haven't hatched that type of egg before).
When the egg hatches it'll be assigned a random gender. The stats, rarity, and element will depend on it's type.
Improving Gameplay[]
This will contribute to trading and make the game more interesting. Old egg sprites/art can be repurposed and used for this feature.
Math Factor[]
You would have to answer questions to breed pets.