Monday, April 02, 2012

Good Old Fashioned Banking

John needed some small bills because he was traveling. He went into a bank and gave the teller a $100 bill. He told her, "I need some two-dollar bills, ten times as many one-dollar bills, and the rest in five-dollar bills. Assuming she didn't tell him to try his request online instead, how many of each did the teller give him?


  1. 5 two-dollar bills
    50 one-dollar bills
    8 five-dollar bills

  2. Anonymous is correct. It would be an interesting twist to the riddle, if you would change this sentence:

    "I need some two-dollar bills, ten times as many one-dollar bills"

    as follows:

    "I need some one-dollar bills, ten times as many two-dollar bills"

    This will make an interesting situation that there is no solution to the problem that includes $2 and $1 notes, but only 20 x $5 notes. Here is the reasoning for this changed scenario:

    GET TO 100d!!!

    If we assume that John wants at least 1 x 1d bill, thus, (1) is not correct.
    But since that is the only one that works out, John only gets 20 x 5d bills.
    We assume that he gets whole bills only, thus, not 1.57 1d bills or something like that.


    (2) - (5): remainder of 1d and 2d is not divisible by 5, so does not work out.

    (6): Amount of 1d and 2d is over 100d, thus that does not work out.

    We conclude that John gets only 20 x 5d bills and no 1d and 2d bills.

    0 x 1d = 0
    0 x 2d = 0
    20 x 5d = 100

    1 x 1d = 1
    10 x 2d = 20
    undefined x 5d = 79

    2 x 1d = 2
    20 x 2d = 40
    undefined x 5d = 58

    3 x 1d = 3
    30 x 2d = 60
    undefined x 5d = 37

    4 x 1d = 4
    40 x 2d = 80
    undefined x 5d = 16

    5 x 1d = 5
    50 x 2d = 100
    undefined x 5d = -5

    Good puzzle, thanks!


  3. Got it too, though in a weird binary equation way. 2x+10x+5y=100
    now, we know that y is a whole no. therefore, 2.4x must be a whole no. The nearest number that makes the expression whole is if we assume x=5.
    Therefore, using this value in the first equation, we get
    And the rest follows..


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