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Question 16

A sequence of all natural numbers whose second digit (from left to right) is 1, is written in strictly increasing order without repetition as follows. $$11, 21, 31, 41, 51, 61, 71, 81, 91, 110, 111, \ldots$$ Note that the first term of the sequence is 11. The third term is 31, eighth term is 81 and tenth term is 110. The 100th term of the sequence will be


Correct Answer: 1100

There are 9 two-digit terms (11 through 91) and 90 three-digit terms (110-119, 210-219, and so on up to 910-919), together accounting for the first 99 terms. So the 100th term is the smallest four-digit number with second digit 1, which is 1100.

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