Date: Thu, 26 Oct 2006 14:26:23 -0500 (CDT)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-02-FALL@uni.edu
Subject: [810-080-02-FALL] Proof for ATM...

Hi 080 students,

     The proof for the ATM involves 10 dollar increments.

  a  20$   50$   b
--- ----  ---- ---
  0    0     0   0
  1   20
  2   40
            50   1          Prove that for all n >= 40 where n = 10p
  3   60                                               for some integer p,
  4   80                          that there exist natural numbers a, b
  5  100   100   2                    such that
                                                 a20 + b50 = n

     Note the places where you can see a difference of 10 dollars.

     Your inductive step will involve finding

        natural numbers c and d such that

                c20 + d50 = k + 10

        using the inductive hypothesis (IH) that

                  a20 + b50 = k dollars for some arbitrary k >= 40

                         where k is a multiple of 10 (divisible by ten).

    The homeworks are all moved back one class day to being due
    on Friday and Monday and Wednesday instead of Wed, Fri and Mon.

    Mark