MathDB
abcd Rearrangements

Source: 2015 10A #10

February 4, 2015
geometrygeometric transformationreflectionsymmetryAMC

Problem Statement

How many rearrangements of abcdabcd are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either abab or baba.
<spanclass=latexbold>(A)</span>0<spanclass=latexbold>(B)</span>1<spanclass=latexbold>(C)</span>2<spanclass=latexbold>(D)</span>3<spanclass=latexbold>(E)</span>4 <span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>4