Alice and Bob play a game. Starting with Alice, they alternate in selecting digits for a 6-digit decimal number UVWXYZ that they construct from left to right. Alice chooses U, then Bob chooses V, then Alice chooses W, and so on. No digit can be repeated. Alice wins if UVWXYZ is not a prime. Can Alice always win?
(In reply to re: No Subject
"What if Bob chooses V=3, X=2?"
OK, V=3. Then Alice chooses one of 1,9 on her 2nd turn and takes the other with her last pick, unless Bob chose it, in which case she picks at random.
Regardless, the numbers 1,3,7,9 have been exhausted and Bob's last pick must either be even or 5, giving a composite number.
Also, the problem states that no digit can be repeated, not that that applies here.
Posted by xdog
on 2013-05-28 15:20:32