Unformatted text preview: k + 1 iteration ? Problem 3 : Scientists at the Princeton Genomics Institute have discovered the following process: Given a test tube ±lled with DNA strands, it is possible to insert an enzyme that will connect two end points of stands (possibly of the same strand), and then dissolve. Experiments show every pair of endpoints is equally likely to be joined. If two endpoints of the same strand connect, then a ”DNA cycle” is formed. Suppose that N enzymes are inserted into a test tube with N strands. What is the expected number of DNA cycles that will be formed? Problem 4 : Prove that for every k ≥ 3 there is a number N ( k ) such that for every set  S  ≥ N of points on the plane there is a subset T ⊆ S of size  T  = k , such that all points in T lie on line, or no three points in T lie on the same line....
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 Fall '08
 Jamespotvein
 Math, white balls, Red balls, following process, Mathematics Final Exam, Princeton Genomics Institute

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