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Dwarfes and river

Source: All Russian Olympiad 2017,Day1,grade 9,P3

May 3, 2017
number theorycombinatorics

Problem Statement

There are 100100 dwarfes with weight 1,2,...,1001,2,...,100. They sit on the left riverside. They can not swim, but they have one boat with capacity 100. River has strong river flow, so every dwarf has power only for one passage from right side to left as oarsman. On every passage can be only one oarsman. Can all dwarfes get to right riverside?
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