Who am I? (hint)

I posted the following problem back on December 3. I thought I’d post the solution, but then I decided maybe to just give you a hint. I’ve emboldened each true statement. The other statement in each pair is false. I did a lot of trial and error, making lists of numbers and crossing things off, narrowing it down. I didn’t have a great strategy, so see if you can do better. Can you figure out the number now?

There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.

1a. I have 2 digits
1b. I am even

2a. I contain a “7”
2b. I am prime

3a. I am the product of two consecutive odd integers
3b. I am one more than a perfect square

4a. I am divisible by 11
4b. I am one more than a perfect cube

5a. I am a perfect square
5b. I have 3 digits

3 thoughts on “Who am I? (hint)

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