Pidgey nests should be illegal!Number Theory Level 4
I've discovered a new kind of bird in my park, which is called Pidgey. If you feed it with enough candies, it will grow into a larger bird called Pidgeotto.
For every Pidgey that you catch in the park, the groundskeeper Willow will award you with 3 candies.
For every Pidgey that you catch but return back to Willow, the groundskeeper will still reward you with 1 candy for your efforts.
For each Pidgey, you need precisely 62 candies in order for it to grow into a Pidgeotto.
If I have no Pidgey nor candies at the start, what is the minimum number of Pidgeys I need to catch in order to have enough candies to grow 10 Pidgeottos?