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CSC 236               Tutorial Exercises for Week  3              Fall 2007
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A.  Make a conjecture about the values of n for which n^2 <= 2^n.
    Prove your conjecture.

B.  When computing the product of n distinct real numbers a_1 a_2 ... a_n,
    there are many ways to order the multiplication operations that have to
    be performed.  For example, the product of a_1 a_2 ... a_5 could be
    computed in the order (a_1 * a_2) * ((a_3 * (a_4 * a_5)), or in the
    order a_1 * ((a_2 * (a_3 * a_4)) * a_5), or in many other ways.

    Make a conjecture about the number of multiplication operations
    required to compute the product a_1 a_2 ... a_n of n distinct real
    numbers, for any n -- in particular, does this number depend on the
    order of the multiplications?
    Prove your conjecture.