One hundred animals for a thousand dollars

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A farmer spends exactly $1000 on exactly 100100 animals, buying at least one of each kind: cows at $50, sheep at $10, and chickens at $0.50 each. How many chickens does he buy?

Show hints (2)+
  1. Two equations: c+s+h=100c+s+h=100 and 50c+10s+0.5h=100050c+10s+0.5h=1000. Eliminate hh.
  2. 99c+19s=190099c+19s=1900; mod 1919 forces c=19c=19, then s=1s=1, h=80h=80.

Answer

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80

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Asked at: Jane Street, Citadel

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