olymmath

IMO 1966 Problem 5

  • Day 2

Solve the system of equations ∣a1−a2∣x2+∣a1−a3∣x3+∣a1−a4∣x4=1|a_1-a_2|x_2+|a_1-a_3|x_3+|a_1-a_4|x_4=1 ∣a2−a1∣x1+∣a2−a3∣x3+∣a2−a4∣x4=1|a_2-a_1|x_1+|a_2-a_3|x_3+|a_2-a_4|x_4=1 ∣a3−a1∣x1+∣a3−a2∣x2+∣a3−a4∣x4=1|a_3-a_1|x_1+|a_3-a_2|x_2+|a_3-a_4|x_4=1 ∣a4−a1∣x1+∣a4−a2∣x2+∣a4−a3∣x3=1|a_4-a_1|x_1+|a_4-a_2|x_2+|a_4-a_3|x_3=1 where a1,a2,a3,a4a_1, a_2, a_3, a_4 are four different real numbers.

Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.

Official text: IMO 1966 official English paper, page 1.

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