Let f be a function defined on all real numbers such that for all x, we have f(x + 5) ≥ f(x) + 5, and f(x + 1) ≤ f(x) + 1. If f(1) = 1, find f(2025).
There are 8 people that need to cross a river. The water is too deep and fast to walk or swim across, and the only transportation device available is a raft. The raft can only be operated by adults, cannot float across the river on its own, and can carry at most two people.
The 8 people are a juvenile delinquent, her jailer, and a dysfunctional family of six: mother, father, two sons, and two daughters. To be clear, the only adults are the jailer, the mother, and the father.
Unfortunately some people fight with each other:
The juvenile delinquent will fight with anybody if her jailer is not present.
The father fights with either daughter if the mother is not present to mediate.
The mother fights with either son if the father is not present to mediate.
How can these 8 people cross the river without any fights? How many trips on the raft did it take?
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