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0, 1, 2, ..., 9 are written in some order on the circumference

Source: 1999 Estonia National Olympiad Final Round grade 12 p5

March 11, 2020
circlenumbersconsecutiveSumnumber theorycombinatorics

Problem Statement

The numbers 0,1,2,...,90, 1, 2, . . . , 9 are written (in some order) on the circumference. Prove that a) there are three consecutive numbers with the sum being at least 1515, b) it is not necessarily the case that there exist three consecutive numbers with the sum more than 1515.
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