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?
Bob's choice for Z can't be 0,2,4,5,6,8 so by choosing 3 of 1,3,7,9 for U,W,Y Alice can force Bob's last choice.
That makes 24 possibilities for UWYZ and 30 for VX or 720 in all, maybe too many for a comfortable search by hand but a snap for a program. If no primes are found, the answer is 'Yes'.
Posted by xdog
on 2013-05-27 16:11:43