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.
For Alice to say that Bob did not know Tanya's number, she would have to know that the tens digit was either 2, 4, 7, or 9:
21 or 28
42 or 49
70 or 77
91 or 98
However, if it was 2 or 9, then Bob would not be able to know what the number was since the same ones digits matched for either 2 or 9:
21 or 91
28 or 98
That leaves 42, 49, 70, and 77.
We can eliminate the first two, because if with Alice holding either a 2 or 9, Bob would have to be holding a 4 with no way of knowing what Alice held.
So Alice must have had a 0 or a 7. If she held a 7, then she would not have been able to conclude that Bob did not know the number because if Bob had a 0, he would already know. Thus, Alice held a 0 and Bob held a 7.
Tanya's number is 70.

Posted by hoodat
on 20160628 04:43:30 