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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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