Question 181
Pablo was trying to solve the following problem: find the sequence $x_0, x_1, x_2, \ldots, x_{2003}$ which satisfies $x_0 = 1$, $0 \leq x_i \leq 2 x_{i-1}$ for $1 \leq i \leq 2003$ and which maximises $S$. Unfortunately he could not remember the expression for $S$, but he knew that it had the form $S = \pm x_1 \pm x_2 \pm \ldots \pm x_{2002} + x_{2003}$. Show that he can still solve the problem.