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)