BARS::McLean to Hamilton via US Hwy-136 in Illinois

Shortly after the Spring 2008 semester ended, RoadHacker drove from Joliet, Illinois, to Warsaw, Illinois. The first 114 miles of the roadtrip was from Joliet to McLean via I-55. At McLean, we headed west 124 miles on US Hwy-136 to Hamilton. At Hamilton, we went south seven miles on Warsaw-Hamilton Road to Warsaw (pop. 1800).

The following is an imaginary road sign that could have existed along westbound US Hwy-136 at McLean.

The imaginary road sign says...

   +----------------------+   (populations)
   | San Jose          23 |   (696)
   | Havana            47 |   (3577)   [Mason County seat]
   | Duncans Mills     57 |   (301)
   | Ipava             64 |   (506)
   | Table Grove       70 |   (396)
   | Adair             75 |   (426)
   | Macomb            87 |   (18,558) [McDonough County seat]
   | Colchester        94 |   (1493)
   | Tennessee         97 |   (144)
   | Carthage         113 |   (2725)   [Hancock County seat]
   | Elvaston         119 |   (152)
   | Hamilton         124 |   (3029)
   +----------------------+

   * mileages from Maps.Yahoo.com
   * census 2000 populations from Wikipedia.org except for 
     Adair and Duncans Mills via BestPlaces.net
   the numbers are:  23  47  57  64  70  75  87  94  97  113  119  124

   enter sandbox (math playground)...

      square number:  64 [sqrt(64) = 8]
      prime numbers:  23  47  97  113
         97 + 47 - 23 = 121  [sqrt(121) = 11]

      prime factorizations:  
         124 = 2 * 2 * 31
         119 = 7 * 17
          94 = 2 * 47
          87 = 3 * 29
          75 = 3 * 5 * 5
          70 = 2 * 5 * 7
          57 = 3 * 19

      124 - 119 = 5 ... 70 / 5 = 14
      113 - 94 = 19 ... 57 / 19 = 3
      87 - 75 = 12

      the numbers become:  3  8  11  12  14

      11 + 14 = 25 [sqrt(25) = 5]
      12 - 3 = 9   [sqrt(9)  = 3]
      5 + 3 = 8

      We've got a BARS!

   ...exit sandbox

   the numbers are:  23  47  57  64  70  75  87  94  97  113  119  124

   the math is: 
      sqrt(64) = sqrt(sqrt(97 + 47 - 23) + (70 / (124 - 119))) + 
                 sqrt(87 - 75 - (57 / (113 - 94)))

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 18 May 2008

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