David, I can't remember the last time I saw A.P. used as an abbrev. to mean arithmetic progression — quite possibly I never did. It took me maybe 3 minutes before I thought of that (which I presume is what you mean, right?). Maybe next time you can spell it out — or abbreviate it like "arith. prog." — the first time with e.g. "A.P." in parentheses, and then use A.P. after that? (At first I thought it was probably some common abbrev. in number theory, a subject I don't have a lot of knowledge about.) Thanks, Dan
On Aug 12, 2015, at 9:22 PM, David Wilson <davidwwilson@comcast.net> wrote:
Consider a game in which two players, A and B, each choose distinct integers by turn.
A's object is to maximize the length of the longest A.P. among his selected integers.
B's object is to limit the length of A's longest A.P.
Show that B cannot prevent A from obtaining an A.P. of length 3.
Can B prevent A from obtaining an A.P. of some length N?
What is the smallest such N?