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HMMT 2012 S3

  • Team 2
  • Answer

Mac is trying to fill 2012 barrels with apple cider. He starts with 0 energy. Every minute, he may rest, gaining 1 energy, or if he has nn energy, he may expend kk energy (0≤k≤n)(0 \leq k \leq n) to fill up to n(k+1)n(k+1) barrels with cider. What is the minimal number of minutes he needs to fill all the barrels?

Dataset text NuminaMath olympiads. Quoted with source.

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