All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
UVWXYZ (Posted on 2013-05-27) Difficulty: 4 of 5
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?

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
No Subject | Comment 6 of 12 |
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
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information