Sweet and Smooth!
Source: EMC 2023 Juniors P4
December 18, 2023
emcalgebraInequality2023
Problem Statement
We say that a -tuple of nonnegative integers (a_1,\hdots,a_{2023}) is sweet if the following conditions hold:
[*] a_1+\hdots+a_{2023}=2023
[*] \frac{a_1}{2}+\frac{a_2}{2^2}+\hdots+\frac{a_{2023}}{2^{2023}}\le 1
Determine the greatest positive integer so that a_1+2a_2+\hdots+2023a_{2023}\ge L holds for every sweet -tuple (a_1,\hdots,a_{2023})Ivan Novak