theblackkeys
10-24-2007, 08:28 PM
Department of Mathematics & Statistics
CSU, Long Beach
Dr. Robert Mena
&
Dr. William Murray
Speaking on:
On Girls Wearing Sweaters: A Pretty Problem with a Pretty Solution
Friday October 26, 2007 12:00noon-1:00PM FO3-200A
Abstract:
Once upon a time, in the icy village of St. Yves lived 7 girls: Alison, Brenda, Chloe, Daphne, Emma, Fiona and Gabrielle. Each girl had 7 sweaters, one in each of seven colors: Orange, Purple, Rose, Scarlet, Turquoise, Wintergreen and Yellow.
Every Saturday when they go to the movies, each of the inseparable friends will wear one sweater. They have a ritual. The following Saturday to a given one, all of the girls will wear the same color sweater as the previous week, except for the follower (who is chosen at random for that week) who will wear a sweater of the same color as the leader (a different girl also chosen at random each week).
At the first movie each season the girls wear sweaters of different colors. Two questions:
1 In the long run what will occur?
2 How many weeks should one expect it will take before that happens?
A little reflection will lead to the answer of question 1. (For example, after the first week, the first follower’s original color is never seen again.) As it turns out, question 2 has a nice answer but to prove it in the general case of girls is slightly problematic. The talk will exhibit the outline of the general proof and it should be accessible to anyone who has a finished a course in matrix theory and has some basic understanding of probability (247 and 380 in CSULB terms).
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Unfortunately I'm not sure if I can go to this presentation, but was wondering if you guys wanted to work on this proof. Is this an interesting problem?
CSU, Long Beach
Dr. Robert Mena
&
Dr. William Murray
Speaking on:
On Girls Wearing Sweaters: A Pretty Problem with a Pretty Solution
Friday October 26, 2007 12:00noon-1:00PM FO3-200A
Abstract:
Once upon a time, in the icy village of St. Yves lived 7 girls: Alison, Brenda, Chloe, Daphne, Emma, Fiona and Gabrielle. Each girl had 7 sweaters, one in each of seven colors: Orange, Purple, Rose, Scarlet, Turquoise, Wintergreen and Yellow.
Every Saturday when they go to the movies, each of the inseparable friends will wear one sweater. They have a ritual. The following Saturday to a given one, all of the girls will wear the same color sweater as the previous week, except for the follower (who is chosen at random for that week) who will wear a sweater of the same color as the leader (a different girl also chosen at random each week).
At the first movie each season the girls wear sweaters of different colors. Two questions:
1 In the long run what will occur?
2 How many weeks should one expect it will take before that happens?
A little reflection will lead to the answer of question 1. (For example, after the first week, the first follower’s original color is never seen again.) As it turns out, question 2 has a nice answer but to prove it in the general case of girls is slightly problematic. The talk will exhibit the outline of the general proof and it should be accessible to anyone who has a finished a course in matrix theory and has some basic understanding of probability (247 and 380 in CSULB terms).
/////////////
Unfortunately I'm not sure if I can go to this presentation, but was wondering if you guys wanted to work on this proof. Is this an interesting problem?