s155sp16MT1.pdf - 1 Stat 155 Spring 2016 MIDTERM EXAM 1...

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1Stat 155 Spring 2016MIDTERM EXAM 1February 22, 2015NAME:SID:The exam isclosed book (no notes)and will be80 minuteslong.You are allowed the use of a calculator that cannot communicate with any other device (no phones!).The test begins on the next page. Please do not write below this line. There is an extra page at the end of thetest.Please SHOW YOUR WORK. No work, NO credit.SCORE/57
2Name:(14 points)1. Indicate which of the following games arenotprogressively bounded impartial combinatorial games, and brieflyexplain why.(2 points each)(a) Poker (standard 5 card draw)(b) Rock-Paper-Scissors(c) Wytho’s Nim (2 pile Nim, and in addition, players may remove equal numbers of chips frombothpilesin a single move)2.(a) Find the Nim sum of 17, 23, and 25.(3 points)(b) In a subtraction game, players may remove 3, 5, or 7 chips on each turn. Find the P positions (the patternsuffices, no proof needed). Which player will win if the starting position has 99 chips?(5 points)
3Name:(6 points)

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