Question 24
Positive integers $a,$ $b,$ and $c$ are chosen so that $a \lt b \lt c,$ and the system of equations $$
2x + y = 2003
$$ and $$
\begin{aligned} &y = |x - a| + |x - b| \\ &\quad {}+ |x - c| \end{aligned}
$$ has exactly one solution. What is the minimum value of $c?$
2x + y = 2003
$$ and $$
\begin{aligned} &y = |x - a| + |x - b| \\ &\quad {}+ |x - c| \end{aligned}
$$ has exactly one solution. What is the minimum value of $c?$