MathDB

11.8

Part of 2021 Ukraine National Mathematical Olympiad

Problems(1)

max no of grams that can weigh 101 weights, each from 1 to 2020 grams

Source: 2021 Ukraine NMO 11.8

4/4/2021
There are 101101 not necessarily different weights, each of which weighs an integer number of grams from 11 g to 20202020 g. It is known that at any division of these weights into two heaps, the total weight of at least one of the piles is no more than 20202020. What is the largest number of grams can weigh all 101101 weights?
(Bogdan Rublev)
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