MathDB

Viktor and Natalia bought

2020

buckets of ice-cream and want to organize a degustation schedule with

2020

rounds such that: - In every round, both of them try

1

ice-cream, and those

2

ice-creams tried in a single round are different from each other. - At the end of the

2020

rounds, both of them have tried each ice-cream exactly once. We will call a degustation schedule fair if the number of ice-creams that were tried by Viktor before Natalia is equal to the number of ice creams tried by Natalia before Viktor. Prove that the number of fair schedules is strictly larger than

2020!(2^{1010} + (1010!)^2)

.
Proposed by Viktor Simjanoski, Macedonia

Problem Statement