|© | Dror Bar-Natan: Classes: 2004-05: Math 157 - Analysis I:||(53)||
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Important! Next week tutorials (December 6, 2004, one time only) will take place as follows: Shay's group at SF 1101, Derek's at BA 1190 and Brian's at BA 1130.
Required reading. All of Spivak's Chapters 12 and 13.
To be handed in. From Spivak Chapter 13: Problems 1, 7 (even parts), 8 (even parts), 13 and 37.
Recommended for extra practice. From Spivak Chapter 13: Problems 5, 7 (odd parts), 8 (odd parts), 9, 15 and 39.
Just for fun. The game of 15 is played as follows. Two players alternate choosing cards numbered between 1 and 9, with repetitions forbidden, so the game ends at most after 9 moves (or rounds). The first player to have within her/his cards a set of precisely 3 cards that add up to 15 wins.
Does this game has a winning strategy? What is it? Who wins, the first to move or the second?
I heard this problem from a student in my other class, Jacob Tsimerman; he heard from a former UofT student, Ravi Vakil, who heard it from Eric Mendelsohn. It may have a longer history, though. (The cards are from http://www.jfitz.com/cards/).
Hint. The first player marks X's, the second marks O's: