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a race with 5 boxes and length 1998 kms

Source: 1998 Estonia National Olympiad Final Round grade 9 p3

November 4, 2020
algebranumber theorycombinatorics

Problem Statement

On a closed track, clockwise, there are five boxes A,B,C,DA, B, C, D and EE, and the length of the track section between boxes AA and BB is 11 km, between BB and CC - 55 km, between CC and DD - 22 km, between DD and EE - 1010 km, and between EE and AA - 33 km. On the track, they drive in a clockwise direction, the race always begins and ends in the box. What box did you start from if the length of the race was exactly 19981998 km?