The Dots and Boxes Game: Sophisticated Child's Play was the title of Elwyn Berlekamp's Arnold Ross Lecture April 21st at the St. Louis Science Center. Berlekamp, mathematics professor at the University of California, Berkeley, was introduced by Bob Devaney, former chair of the Arnold Ross Lectures Series committee, who called him "one of the outstanding scientists in the country, well known for his ability to communicate the beauty and wonder of contemporary mathematics."
Berlekamp began his lecture by noting that when he was growing up, he often played Dots and Boxes during class, and told the audience that he wouldn't mind if any of them played during his talk -- perhaps they would discover a new theorem about the game. To play the game, two players alternate drawing horizontal or vertical lines which connect dots in a rectangular grid. When a player draws a segment that completes a box, he or she gets that box and another turn; the player with the most boxes at the end of the game wins. The rules may be simple but the theorems and strategy presented in the lecture were sophisticated, involving graph theory, duals, chains, and loops. Berlekamp did highlight two or three basic strategies that could help players beat almost any opponent.
After his lecture, Professor Berlekamp simultaneously played about a dozen members of the audience in Dots and Boxes. He offered 50 dollars to anyone who could beat him. Although the students played well, and had fun, none collected the money.
Five students collected a total of \$7000 from the AMS in the game Who Wants To Be A Mathematician, following the talk. Jason Wu and Alex Song from Ladue Horton Watkins High School each won \$2000, and, in a shorter round, Gerardo Flores, also from Ladue, and Jon Potts and Alex Schiller, from Mary Institute and St. Louis Country Day School each won \$1000.
The two \$2000 winners both used their 50-50 and Ask Your Teacher lifelines on their final question. Jim Moser, their teacher, gave them sound and valuable advice as each contestant was inclined toward the remaining wrong answer before consulting Moser. His choices and clear explanations carried the day for his students, who both took his advice.
St. Louis television station KSDK-Channel 5 aired a segment from the game on their evening news that day showing the game and Jason winning the grand prize. The ten Who Wants To Be A Mathematician contestants are pictured below.
Contestant names and prizes:
Jason Wu and Alex Song, Ladue Horton Watkins High School: \$2000 from the AMS, Maplesoft's Maple 9.5, TI 89 Titanium graphing calculators from Texas Instruments, Anton's Calculus and access to the Machina website from John Wiley and Sons, What's Happening in the Mathematical Sciences, one-year subscriptions to the Mathematical Association of America (MAA) journals The College Mathematics Journal and Horizons, five AMS T-shirts, two books from the MAA, Mathematical Impressions by Anatolli Fomenko, an MAA T-shirt, a pass to the Omnimax theater from the St. Louis Science Center, and Elwyn Berlekamp's Dots and Boxes (donated by A.K. Peters).
Jon Potts and Alex Schiller, Mary Institute and St. Louis Country Day School; and Gerardo Flores, Ladue Horton Watkins High School: \$1000 from the AMS, Maplesoft's Maple 9.5, Anton's Calculus and access to the Machina website, What's Happening in the Mathematical Sciences, one-year subscriptions to The College Mathematics Journal and Horizons, Mathematical Impressions by Anatolli Fomenko, and Elwyn Berlekamp's Dots and Boxes.
Eric Nieters, Governor French Academy: An AMS T-shirt, an MAA T-shirt, a pass to the Omnimax theater from the St. Louis Science Center, and Elwyn Berlekamp's Dots and Boxes.
Dale Trantham and Nick Little, Ozark High School: One-year subscriptions to The College Mathematics Journal and Horizons, Mathematical Impressions by Anatolli Fomenko, and Elwyn Berlekamp's Dots and Boxes.
Justin Myers, Nixa High School; and Michael Kramer, Mary Institute and St. Louis Country Day School: Elwyn Berlekamp's Dots and Boxes.
Each contestant also received a T-shirt from Maplesoft, planetarium tickets from the St. Louis Science Center, an icosahedron from the MAA, and a briefcase from the AMS.
The Arnold Ross Lectures are sponsored by the AMS and are held in science museums across the country. Read about the 2003 Arnold Ross Lectureheld in Chicago.