Putting quite a bit of gold in two treasure chests
Source: Bundeswettbewerb Mathematik 2020, Round 2 - Problem 1
November 17, 2020
combinatoricscombinatorics proposedgameCombinatorial games
Problem Statement
Leo and Smilla find gold nuggets with masses gram, which they distribute to a red and a blue treasure chest according to the following rule:First, Leo chooses one of the chests and tells its colour to Smilla. Then Smilla chooses one of the not yet distributed nuggets and puts it into this chest.This is repeated until all the nuggets are distributed. Finally, Smilla chooses one of the chests and wins all the nuggets from this chest.How many gram of gold can Smilla make sure to win?