Problem #PRU-34931

Problems Algebra Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property

Problem

On the dining room table, there is a choice of six dishes. Every day Valentina takes a certain set of dishes (perhaps, she does not take a single dish), and this set of dishes should be different from all of the sets that she took in the previous days. What is the maximum number of days that Valentina will be able to eat according to such rules and how many meals will she eat on average during the day?