BARS::Mileages From the McDonald's in McLean, Illinois

This McDonald's mileage map is in Mclean, Illinois.

The McDonald's mileage map says...

   +--------------------------------------------------+
   | St. Paul      500 Mi.       Chicago      144 Mi. |
   | Denver        900 Mi.       New York     900 Mi. |
   | Los Angeles  1950 Mi.       Atlanta      580 Mi. |
   | St. Louis     160 Mi.       New Orleans  800 Mi. |
   +--------------------------------------------------+

Finding an equation for this mileage map was more difficult than MathBabbler expected. ["Expect the unexpected."]

   the numbers are:  500  900  1950  160  144  900  580  800

   the base-2 math is:
      sqrt(144) - (160 - (1950 - 900 - 900)) = (800 / (580 - 500))base-2

   observe...
      left-side:
         sqrt(144) = 12
         1950 - 900 - 900 = 1050 - 900 = 150
         160 - 150 = 10
         12 - 10 = 2
      right-side:
         580 - 500 = 80
         800 / 80 = 10
         10base-2 = 2

   [to be completed--find math using base-10 only]

   enter math playground...

      square numbers:  144 (12), 900 (30), 900 (30)   

      derived square numbers:  
         160 - 144 = 16 (4)(2)
         500 - 160 - 144 = 196 (14)
         1950 - (500 - 160 - 144) = 1936 (44)

      prime factorizations:
          500 = 2  2                 5  5  5
          580 = 2  2                 5            29
          800 = 2  2  2  2  2        5  5
          900 = 2  2           3  3  5  5
         1950 = 2              3     5  5     13
         ===========================================
                2                    5

      gcf(500, 580, 800, 900, 1950) = 10

      the numbers become:  160  144  10

      hexadecimal math:  160 - 144 = 10base-16
           binary math:  sqrt(sqrt(160 - 144)) = 10base-2

      split_into_squares_sum(160) = { 144, 16 }

      the numbers become:  144  144  16  10

      the math is:  sqrt(144) - sqrt(16 - sqrt(144)) = 10
        more math:  (sqrt(144) + sqrt(144) - sqrt(16)!)! = log(10)
       octal math:  sqrt(144) + sqrt(144) - 16 = 10base-8

   ...exit math playground

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 16 May 2008 (posted 19 May 2008)

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This work is licensed under a Creative Commons Attribution 3.0 United States License.