Library / UKMT Intermediate Mathematical Challenge /264 of 267

UKMT Intermediate Mathematical Challenge, 2018

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A particular integer is the smallest multiple of 72, each of whose digits is either 0 or 1. How many digits does this integer have?

(A) $4$ (B) $6$ (C) $8$ (D) $10$ (E) $12$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.