Modified version of ARML 2011 I-1 Individual Competition in Chicago

Modified set theoretic version of ARML 2011 I-1.
Let S be the set of all natural numbers
that gain a single digit when multiplied by 2.
Find the 600th smallest member of S
S, which is obviously not empty/vacuous, has a minimum value of 5 since 2*5 =10 has one more digit than the single digit five. Well Ordering property of the integers not important for this enumeration via a table combinatorics problem
Math educator Sharon Casador Ruña published solution of the original problem. Gratitude and recognition to the many devoted tutors/teachers in Koronadal City, Philippines
Cape Coral, Florida DWhatley
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