You'll have to forgive me. Having encountered the abbreviation "A.P." in high school, I assumed it was on a par with "GCD" or "LCM" in terms of general familiarity, meaning I didn't need to define it in this forum. Apologies. "A.P." indeed stands for "arithmetic progression". I feel your pain. When I see something I don't understand in this forum, I usually wait for the follow-up messages to clarify the situation, or in the case of analysis geeks spouting about q-equations, Galois groups and hypergeometric functions, politely skip on to the next email. "Better to remain silent and be thought a fool than to speak out and remove all doubt." But seriously, in any mathematical discussion you must assume some background material, which implies that someone is not going to understand what you're talking about.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Thursday, August 13, 2015 1:01 AM To: math-fun Subject: Re: [math-fun] Game question
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?
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