# Infinite game

Author: daniyar
Problem has been solved: 38 times

Русский язык | English Language

An infinite number of people choose different positive integer numbers $k$. For each such player, the host (who is not a player) randomly selects a “winning” unit cube inside the cube $k \times k \times k$. If the player guesses the “winning” die (on one try), he will receive $k$ dollars. It turned out that every $i$'s player chose a number $i$. Let $n$ be the expected value of the amount that all players will win in total. Find $[2020n ^ 2]$, where $[n]$ is the largest integer not exceeding $n$.

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