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Unformatted text preview: MATH 475; EXAM # 1, 100 points, October 11, 2007 (R.A.Brualdi) TOTAL SCORE : Name: These R. Solutions Do not multiply out factorials and combination numbers. Circle your answers. 1. (10 points) What should player Is first move be in the following game of NIM in order that she not lose: Piles of 23, 22, and 12. 23 = 10111 22 = 10110 12 = 01100 Adding base 2 without carrying, we get 01101. So we must remove 11 from the 12-pile to leave 1 (in base 2, 0001) to balance the game and be assured of winning. 2. (10 points) The Overture Center has performance halls with seat capacities of 1200, 800, 600, 400, and 200 (I am making this up!). How many people must attend a performance on a given night in order that at least one of the performance halls is more than half full? 600 + 400 + 300 + 200 + 100 + 1 = 1601 2. A series of counting problems (10 points each) (a) In how many ways can 10 women and 4 men line up in a straight line so that no two men are consecutive?...
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