CHEM 115 Final: CHEM 115 UMass Boston FinalExamSample
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There are ve problems on this exam, each worth 20 points, for a total of 100 points. You have approximately three hours to complete this exam. Let {0, 1}n be the set of all binary strings x1x2 . xn of length n. For any string x in {0, 1}n, let r(x) = xnxn 1 . x1 be the reversal of x. Let x y if x = y or x = r(y). Given a string x in {0, 1}n and a permutation of {1, . , n}, let (x) be the string x (1), x (2), . Let x y if there exists some such that x = (y). Solution: given a string x, the equivalent class [x] = {x, r(x)} has either one element (if x = r(x)) or two elements (if x 6= r(x)). Let m1 be the number of one-element classes and m2 the number of two-element classes.
