Math Gold Medalist

Lor

2022 AMC 12B 

Problem 1

Define $x\diamond y$ to be $|x-y|$ for all real numbers $x$ and $y.$ What is the value of\[(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?\]

$\textbf{(A)}\ {-}2 \qquad \textbf{(B)}\ {-}1 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 1 \qquad \textbf{(E)}\ 2$

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   Solution