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Absolute computation

Source: 2022 AMC 10B#1/AMC 12B #1

November 17, 2022
AMCAMC 10AMC 122022 AMC2022 AMC 10B2022 AMC 12B

Problem Statement

Define x⋄yx\diamond y to be ∣x−y∣|x-y| for all real numbers xx and yy. What is the value of (1⋄(2⋄3))−((1⋄2)⋄3)?(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?
<spanclass=′latex−bold′>(A)</span> −2<spanclass=′latex−bold′>(B)</span> −1<spanclass=′latex−bold′>(C)</span> 0<spanclass=′latex−bold′>(D)</span> 1<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ -2 \qquad <span class='latex-bold'>(B)</span>\ -1 \qquad <span class='latex-bold'>(C)</span>\ 0 \qquad <span class='latex-bold'>(D)</span>\ 1 \qquad <span class='latex-bold'>(E)</span>\ 2
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