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min 4-digit , when divided by 3 gives a 4-digit number with the same digits

Source: 2004 Austria Beginners' Competition p1

October 4, 2022
number theoryDigits

Problem Statement

Find the smallest four-digit number that when divided by 33 gives a four-digit number with the same digits. (Note: Four digits means that the thousand Unit digit must not be 00.)