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MathNet 2020 — Math Olympiad Vault — Part 06 Question 63

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 06

Question 63

Given $n$ pairwise distinct positive numbers. Vasia wrote on the board all possible numbers of the form $a + \frac{b}{c}$, where $a, b, c$ are distinct numbers from the given set. Can one always find two numbers on the board such that the larger one is not more than twice the other one, if

a) $n=4$?

b) $n=3$?