Call a rational number short if it has finitely many digits in its decimal expansion. For a positive integer m, we say that a positive integer t is m−tastic if there exists a number c∈{1,2,3,…,2017} such that c⋅m10t−1 is short, and such that c⋅m10k−1 is not short for any 1≤k<t. Let S(m) be the set of m−tastic numbers. Consider S(m) for m=1,2,…. What is the maximum number of elements in S(m)? IMO Shortlistnumber theorydecimal representationDigitsIMOIMO 2017