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AMC10 #25 A confusing "elevenses"

Source: 2017 AMC 10A #25

February 8, 2017
AMCAMC 102017 AMC 10Acounting

Problem Statement

How many integers between 100100 and 999999, inclusive, have the property that some permutation of its digits is a multiple of 1111 between 100100 and 999999? For example, both 121121 and 211211 have this property.
<spanclass=latexbold>(A)</span>226<spanclass=latexbold>(B)</span>243<spanclass=latexbold>(C)</span>270<spanclass=latexbold>(D)</span>469<spanclass=latexbold>(E)</span>486 <span class='latex-bold'>(A) </span>226\qquad <span class='latex-bold'>(B) </span> 243 \qquad <span class='latex-bold'>(C) </span> 270 \qquad <span class='latex-bold'>(D) </span>469\qquad <span class='latex-bold'>(E) </span> 486