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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).
(No Solution Yet, 2 Comments) Submitted on 2025-03-18 by Danish Ahmed Khan   
Difficulty: 3 of 5 Bonus: Dysfunctional Crossing (in Logic) Rating: 4.15
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?

    For a fun way to test out your theories, click here and then click on the blue circle.

    (Solution Posted, 32 Comments) Submitted on 2005-09-26 by nikki   
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