Heads, Tails, and a Row of Coins
Number Theory · 26th PMO Qualifying Stage
There are 2024 coins laid out in a row. For some positive integer $x$, at least $\dfrac{2}{3}$ of the first $x$ coins are heads, and at least $\dfrac{4}{5}$ of the last $x$ coins are tails. What is the maximum possible value of $x$?
A$1012$
B$1079$
C$1288$
D$1380$