# Absolute Value System

Algebra Level 4

\begin{aligned} |a - b | &=& 2 \\ |b - c | &=& 3 \\ |c - d | &=& 4 \\ \end{aligned}

Given that $a,b,c,d$ are real numbers that satisfy the system of equations above, what is the sum of all distinct values of $|a-d|$?

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