MathDB
Bambula carries weights

Source: Saint Petersburg olympiad 2024, 9.2

September 21, 2024
algebracombinatorics

Problem Statement

A strongman Bambula can carry several weights at the same time, if their total weight does not exceed 200200 kg, and these weights are no more than three. On the way to work, he injured his finger and found that he could now carry no more than two weights (and still no more than 200200 kg). At what minimum kk is the statement true: any set of 100100 weights that Bambula could previously carry in 5050 runs, with a sore finger, he will be able to carry in no more than kk runs?