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Homework Assignment 12

Assigned Tuesday November 30; due Wednesday December 8, 2PM, at SS 1071
(though no penalty for late assignments, up to Friday December 10, 2PM)

this document in PDF: HW.pdf

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 $ 4\frac12$ 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:

4 9 2
3 5 7
8 1 6

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Dror Bar-Natan 2004-12-01