Hi All,

This is a really poorly-worded question, but I think the 'intent' of this question is to describe an increasing sequence of positive integers in which every integer that includes at least one 3 among its digits is in the sequence (so the numbers 3, 33, 153, 337, etc. would all be in the sequence). Assuming that the first term in the sequence is "3", we're asked to find the 150th term in the sequence.

From 1 to 99, there are 19 terms that contain at least one '3' (you can list them out - it's not hard to find them)

From 100 to 199, there are 19 terms that contain at least one '3' (you can list them out if needed)

From 200 to 299, there are 19 terms that contain at least one '3' (you can list them out if needed)

So far, there are 3(19) = 57 terms accounted for. Once we hit 300, EVERY term in the next 100 terms will contain at least one '3', so we need to go 93 terms 'in' to this set of 100 terms to find that 150th term... Starting at 300, 93 terms in would be 392.

Final Answer:

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