Question 24
Determine the maximum value of the following expression, where $x_1,x_2,\ldots,x_{2014}$ are distinct numbers in the set $\{1,2,3,4,\ldots,2014\}$.
**Source-display uncertainty.** The operation delimiters and set braces are damaged in the supplied PDF. The solution suggests the nested-absolute-value expression
$$\left|\cdots\left|\left|x_1-x_2\right|-x_3\right|-\cdots-x_{2014}\right|.$$
To specify this inferred reading without ambiguous nesting, let $y_1=x_1$ and $y_j=|y_{j-1}-x_j|$ for $j=2,\ldots,2014$; the requested expression would be $y_{2014}$. This reconstruction is provisional and requires source confirmation.
**Source-display uncertainty.** The operation delimiters and set braces are damaged in the supplied PDF. The solution suggests the nested-absolute-value expression
$$\left|\cdots\left|\left|x_1-x_2\right|-x_3\right|-\cdots-x_{2014}\right|.$$
To specify this inferred reading without ambiguous nesting, let $y_1=x_1$ and $y_j=|y_{j-1}-x_j|$ for $j=2,\ldots,2014$; the requested expression would be $y_{2014}$. This reconstruction is provisional and requires source confirmation.