Pidgey nests should be illegal!
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 .
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For every Pidgey that you catch in the park, the groundskeeper Willow will award you with 3 candies.
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For every Pidgey that you catch but return back to Willow, the groundskeeper will still reward you with 1 candy for your efforts.
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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?
The answer is 158.
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1 solution
It will take 620 candies to grow 10 Pidgeotto. If we set the number of Pidgey caught to be n, then 620=3n+(n-10)=4n-10, because you get 3 candies for each Pidgey caught and can send all but 10 away for 1 more each. Solving leads to n=157.5, rounding up leads to the answer of 158 Pidgey.