Difference between revisions of "KGS math club"

Revision as of 21:55, 20 June 2008

A group of people on Kiseido Go Server Mathematics room.

The meaning of this page is to collect the problems posed there and save hints and solution suggestions.

KGS math problems
Date	Author	Problem	Solutions
20.2.2007	StoneTiger	Does any member of the sequence 1, 4, 20, 80, ... generated by x(n) = 6x(n-1) - 12x(n-2) + 8x(n-3) ever have a factor in common with 2007?	sigmundur
21.6.2008	amkach	Consider the two player game that begins with an even length sequence of positive integers. Each player, in turn, removes either the first or last of the remaining integers, ending when all the integers have been removed. A player's score is the sum of the integers that they removed; the winner is the player with the higher score (with a tie if equal scores). Show that Player One has a non-losing strategy, i.e., can always force a tie or a win.

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-|Consider the two player game that begins with an even length ordered sequence of positive integers.  Each player, in turn, removes either the first or last of the remaining integers, ending when all the integers have been removed.  A player's score is the sum of the integers that they removed; the winner is the player with the higher score (with a tie if equal scores).  Show that Player One has a non-losing strategy, i.e., can always force a tie or a win.
+|Consider the two player game that begins with an even length sequence of positive integers.  Each player, in turn, removes either the first or last of the remaining integers, ending when all the integers have been removed.  A player's score is the sum of the integers that they removed; the winner is the player with the higher score (with a tie if equal scores).  Show that Player One has a non-losing strategy, i.e., can always force a tie or a win.
 |style="background-color:rgb(220,230,255);" |