2021 JMPSC Sprint Problems/Problem 17
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Problem
What is the smallest positive multiple of that has no zeros in its decimal representation?
Solution
Notice that . Since
always has
zeros after it, we have to make sure
has
nonzero digits, so that the last 3 digits of the number
doesn't contain a
. We also need to make sure that
has no zeros in its own decimal representation so that
doesn't have any zeros other than the last
digits. The smallest number
that satisfies the above is
, so the answer is
.
~Mathdreams
~edited by tigerzhang
See also
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