tag:blogger.com,1999:blog-4479690110975267663.post6380353423719797117..comments2024-01-19T01:16:30.000-08:00Comments on Albany Area Math Circle: Don't lose ALL your marbles!Mary O'Keeffehttp://www.blogger.com/profile/14662977706706048151noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-4479690110975267663.post-84231294560882034152011-02-04T21:01:05.640-08:002011-02-04T21:01:05.640-08:00Hint: Look for an attribute of the marbles that is...Hint: Look for an attribute of the marbles that is conserved by all the allowed operations.<br /><br />Parity (i.e., evenness or oddness) is a good attribute to consider. Is it ever possible to have an odd number of white marbles/black marbles/total marbles?<br /><br />You also want to consider boundary conditions? Is it ever possible to reduce the total number of marbles to zero? Is it ever possible to reduce the total number of black marbles to zero? What about reducing the total number of white numbers to zero?Mary O'Keeffehttps://www.blogger.com/profile/14662977706706048151noreply@blogger.com