olymmath

OPM 1997 Problem 6

  • Final day 2

nn parallel segments of lengths a1≤a2≤a3≤...≤ana_1 \le a_2 \le a_3 \le ... \le a_n were painted to mark an airport atrium. However, the architect decided that the nn segments should have equal length. If the cost per meter of extending the lines is equal to the cost of reducing them, how long should the lines be in order to minimize costs?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Portuguese Mathematical Olympiad 1997 official paper, page 1.

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