On April 16, 2015, Tanya Khovanova wrote in her blog:
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?
(In reply to re(2): could be
Both you and Charlie are determined to answer Tanya's question, and do not address my request to comment upon the text of the puzzle.
1. Assuming that both A and B are very logical people, and the task assigned to them (not explicitly stated in the text) was to find out T's number, A - being told that the units' digit is 0 (or 7) would spell out loud and clear :" The number is 70 (77)" and not tease B: "You don't know the number", realizing a priori that her announcement will be followed by "Now I know!".
2. Charlie is a logical person. His comprehensive list includes all 7*k numbers below 100. The first number is 7, not 07. Nothing being specified about inclusion of leading zeroes - the default representation is 7 - and 07 should have been excluded by both logical participants. If it were allowed- Bob would be the first to speak without need of any additional information.
3. As usual, once the puzzle is not strictly defined - it's up to the solver to specify the clarifications (= the way he sees them).
4. Now it is up to you - could this conversation take place?
If yes, upon what assumptions?
Please comment on the puzzle after reading the above.
Edited on May 10, 2016, 10:01 pm