[math-fun] Putnam mis-reading
Hi all, I'm probably not alone on this list in that I like to try my hand at the Putnam problems each year. This past December, problem A2 was the following... Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008x2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is non-zero; Barbara wins if it is zero. Which player has a winning strategy? This is not an overly challenging problem. Unfortunately for me, I misread the problem and tried to solve the game where Alan is trying to force the zero determinant. This seems a lot more challenging -- I have yet to solve it, though I am pretty convinced I know which player actually has the strategy. Do any math-funners want to give this a try? Dave
Some consolation that --- this year at any rate --- your version would be easier than the official one! WFL On 1/19/09, Dave Blackston <hyperdex@gmail.com> wrote:
Hi all,
I'm probably not alone on this list in that I like to try my hand at the Putnam problems each year. This past December, problem A2 was the following...
Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008x2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is non-zero; Barbara wins if it is zero. Which player has a winning strategy?
This is not an overly challenging problem. Unfortunately for me, I misread the problem and tried to solve the game where Alan is trying to force the zero determinant. This seems a lot more challenging -- I have yet to solve it, though I am pretty convinced I know which player actually has the strategy. Do any math-funners want to give this a try?
Dave _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Really? The "official" version can be solved easily: (rot-13ed) Fvapr 2008 vf rira, Oneonen pna jva ol fvzcyl cnvevat ragevrf [2v, w] naq [2v+1, w]. Jurarire Nyna cynlf n ahzore va ba ragel bs n cnve, Oneonen cynlf gur fnzr ahzore va gur bgure ragel. Guvf sbeprf gur raq zngevk gb or 1004 cnvef bs vqragvpny ebjf, naq gur qrgrezvanag vf pyrneyl 0. I have yet to come up with an answer for my version, though it is entirely possible I am missing something obvious. Dave On Mon, Jan 19, 2009 at 11:13 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Some consolation that --- this year at any rate --- your version would be easier than the official one! WFL
On 1/19/09, Dave Blackston <hyperdex@gmail.com> wrote:
Hi all,
I'm probably not alone on this list in that I like to try my hand at the Putnam problems each year. This past December, problem A2 was the following...
Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008x2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is non-zero; Barbara wins if it is zero. Which player has a winning strategy?
This is not an overly challenging problem. Unfortunately for me, I misread the problem and tried to solve the game where Alan is trying to force the zero determinant. This seems a lot more challenging -- I have yet to solve it, though I am pretty convinced I know which player actually has the strategy. Do any math-funners want to give this a try?
Dave _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Oops -- it seems that misreading is becoming a habit of mine... I agree that my version would be easier than the official version when played on a 2009x2009 grid. Sorry for the misunderstanding... On Mon, Jan 19, 2009 at 11:13 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Some consolation that --- this year at any rate --- your version would be easier than the official one! WFL
On 1/19/09, Dave Blackston <hyperdex@gmail.com> wrote:
Hi all,
I'm probably not alone on this list in that I like to try my hand at the Putnam problems each year. This past December, problem A2 was the following...
Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008x2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is non-zero; Barbara wins if it is zero. Which player has a winning strategy?
This is not an overly challenging problem. Unfortunately for me, I misread the problem and tried to solve the game where Alan is trying to force the zero determinant. This seems a lot more challenging -- I have yet to solve it, though I am pretty convinced I know which player actually has the strategy. Do any math-funners want to give this a try?
Dave _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (2)
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Dave Blackston -
Fred lunnon