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Combinatorics Difficulty 2.0 Junior Find the answer Canada

The time on a digital clock reads 3:33. What is the shortest length of time, in minutes, until all of the digits are again equal to each other?

(A) $71$ (B) $60$ (C) $142$ (D) $222$ (E) $111$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.