Steven J Miller sjm1Williamsedu 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 ID: 757708
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Math 331: Problem Solving
Steven J Miller (sjm1@Williams.edu)
Second
Remote Participation Lecture
April 26,
2017Slide2
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?Slide3Slide4Slide5Slide6Slide7Slide8
Move
#1's Money
#2's Money
#1's Bid
#2's Bid
12345678910111213Slide9
Move
#1's Money
#2's Money
#1's Bid
#2's Bid
12345678910111213Slide10
Move
#1's Money
#2's Money
#1's Bid
#2's Bid
12345678910111213Slide11
Move
#1's Money
#2's Money
#1's Bid
#2's Bid
12345678910111213Slide12Slide13Slide14Slide15Slide16
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 4Castle 5Castle 6Castle 7Castle 8Castle 9Castle 10Team 1Team 2OutcomeSlide17
Castle 1
Castle 2
Castle 3
Castle 4
Castle 5
Castle 6Castle 7Castle 8Castle 9Castle 10Team 1Team 2OutcomeSlide18
Castle 1
Castle 2
Castle 3
Castle 4
Castle 5
Castle 6Castle 7Castle 8Castle 9Castle 10Team 1Team 2OutcomeSlide19Slide20Slide21Slide22Slide23Slide24Slide25Slide26Slide27Slide28Slide29Slide30Slide31Slide32Slide33Slide34Slide35Slide36Slide37Slide38Slide39Slide40Slide41Slide42Slide43Slide44Slide45Slide46Slide47Slide48Slide49Slide50Slide51