My friend was thinking of a 3-digit prime number. I asked him, "What are the last two digits of your number?" He answered, and I knew what the number was. What was the number?

The friend was thinking of 389. 

389 is the only 3-digit prime number that ends with the digits 8 and 9.  All other digit pairs exist in more than one 3-digit prime -- except where leading zeroes are permitted, in which case 002 ending in digits 0 and 2, and 005 ending in digits 0 and 5 are also unique digit pairs in 3-digit primes.  Yet, it is inferred the solution is unique, thus the implication is that leading zeroes are not permitted.

 

Posted by Dej Mar on 2011-01-27 18:09:08