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?
Alice selects U=7 and W=1.
If Bob selects V=0,4,5,6 or 8, Alice selects Y=3, forcing Bob to select Z=9. Any X value yields a composite, so Alice wins.
If Bob selects V=2, Alice has only to fear X=4 since 721439 is prime. But in that case she can force 721493 which is composite.
So Alice can always win.
Posted by xdog
on 2013-05-28 10:05:12