Mary poses the question, "What is 40 times the number of digits in the answer to this question?" But then she realizes that it could have two possible answers, namely 80 and 120.
Let's generalize the question: For how many positive integer values would Mary's question above lead to multiple answers? (I.e., what if she replaces the "40" in her question with a positive integer )
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Let n be the number of digits in the answer to the question.
For N < 1 0 0 0 , the only multiple answers could be n = 1 vs 2, n = 2 vs 3, or n = 3 vs 4.
For n = 1 vs 2, we have 5 possibilities, N = 5 through 9. (e.g. For n = 7, both 7 and 14 would be correct answers)
For n = 2 vs 3, we have 16 possibilities, N = 34 through 49.
For n = 3 vs 4, we have 84 possibilities, N = 250 through 333.
5 + 1 6 + 8 4 = 1 0 5