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
re(2): could be by armando)
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
re(3): could be
