Math 331: Problem Solving Steven J Miller

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Presentation transcript:

Math 331: Problem Solving Steven J Miller (sjm1@Williams Math 331: Problem Solving Steven J Miller (sjm1@Williams.edu) Second Remote Participation Lecture April 26, 2017

RECTANGLE GAME: Consider M x N board, take turns, each turn can break any piece along one horizontal or along one vertical, last one to break a piece wins. Does someone have a winning strategy?

Move #1's Money #2's Money #1's Bid #2's Bid 1 2 3 4 5 6 7 8 9 10 11 12 13

Move #1's Money #2's Money #1's Bid #2's Bid 1 2 3 4 5 6 7 8 9 10 11 12 13

Move #1's Money #2's Money #1's Bid #2's Bid 1 2 3 4 5 6 7 8 9 10 11 12 13

Move #1's Money #2's Money #1's Bid #2's Bid 1 2 3 4 5 6 7 8 9 10 11 12 13

Castle game: Have castles labeled 1 through 10 (label is value), divide 100 soldiers to attack the castles against an opponent, whomever sends more to a castle wins it. What strategy is best to get more points than opponent? Castle 1 Castle 2 Castle 3 Castle 4 Castle 5 Castle 6 Castle 7 Castle 8 Castle 9 Castle 10 Team 1 Team 2 Outcome

Team 1 Team 2 Outcome Castle 1 Castle 2 Castle 3 Castle 4 Castle 5

Team 1 Team 2 Outcome Castle 1 Castle 2 Castle 3 Castle 4 Castle 5