# The coffee machine

**Number Theory**Level 3

A University department, with ten professors, is considering buying a coffee machine to put in the professors' room. The machine costs 1000$. The professors are asked, in a private email, how much they are willing to spend, at most, to participate in the purchase and gain the right to use the machine. Each one answers with an amount. What is the minimal sum, in dollars, of these amounts that ensures the formation of a group of participants, of any size, among the professors, able to buy the machine, every participant paying the same amount and spending no more than what they wanted to?

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