At some time in the now distant past, there was a party with 100 guests. The host had bought exactly the same number of drinks for every guest, and for public health reasons, that number was less than seventy-five. During the party, it turned out that seventeen of the guests did not drink at all. The remaining 83 guests all had the same number of drinks, and afterwards, there were 21 drinks left. How many drinks had the host bought? Explain why your answer is the only possible one. Hint: modular arithmetics

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