For some reason I am prompted to ask: what is known about maximal lengths of arithmetic progressions of 0's in the Morse-Thue sequence? I can see some sevens. On Thu, Aug 13, 2015 at 3:45 PM, Tom Rokicki <rokicki@gmail.com> wrote:
Let us say A always chooses the smallest nonnegative integer that has not yet been chosen.
For a given k, what is the longest that B can hang on without A winning? Without loss of generality we can assume B always chooses numbers in an increasing sequence.
On Wed, 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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