On April 16, 2015, Tanya Khovanova wrote in her blog:

<begin>

Here is my new logic puzzle.

I thought of a positive integer that is below 100 and is divisible by 7. In addition to the public knowledge above, I privately tell the units digit of my number to Alice and the tens digit to Bob. Alice and Bob are very logical people, but their conversation might seem strange:

Alice: You do not know Tanya’s number.

Bob: I know Tanya’s number.

What is my number?

<end>

Please comment.

(In reply to

could be by Charlie)

I accept your reasoning till

"...Perhaps Alice saw a 7 and made the judgement that Bob saw a 7 also, but also perhaps, Bob was told either that there was no tens digit or that the tens digit was zero. Maybe despite being very logical, Alice overlooked this possibility when she made her statement...."

IMHO nothing in the puzzle implies:

a. that leading zeroes are allowed

b. that their task was to find the number

Please continue your comment taking my assumptions as facts (even if you do not agree).