### BARS::I-95 North in Bangor, Maine

These road signs are on northbound I-95 in Bangor, Maine.

The road signs say...

```   +--------------+ +-----------------------+
|    North     | |             Exit 182B |
| I-95   ME-15 | | To US-2   ME-100 West |
|    Orono     | |       Hermon          |
|   Houlton    | |      1/4 mile         |
+--------------+ +-----------------------+
+-----------------------------+
|                   Exit 182A |
|        South                |
| I-395  ME-15 to US-1A  ME-9 |
|        Bangor - Brewer      |
+-----------------------------+
```
```   the numbers are:  95  15  182  2  100  1/4  182  395  15  1  9

the math is:
sqrt(9) *
sqrt(15 + 15 + (2 + 1) / sqrt(1/4)) -
sqrt((182 + 182) - (395 - 95)) =
sqrt(100)

observe...
sqrt(9) = 3

(2 + 1) = 3
sqrt(1/4) = 1/2
3 / 1/2 = 3 * 2 = 6
15 + 15 + 6 = 36
sqrt(36) = 6

182 + 182 = 364
395 - 95 = 300
364 - 300 = 64
sqrt(64) = 8
3 * 6 - 8 = 18 - 8 = 10

sqrt(100) = 10

[solve for 'n']
sqrt(9) * n - sqrt((182 + 182) - (395 - 95)) = sqrt(100)

solution:  n = sqrt(15 + 15 + (2 + 1) / sqrt(1/4))
```

RoadHacker took a picture of these road signs because he saw two numbers that were duplicated. 182 and 15 both occur twice; therefore, the math could be trivialized as follows.

```   (182 - 182) = (15 - 15) * (whatever)
i.e. 0 = 0 * (whatever)

What's whatever?  The remaining numbers can be used in any
arithmetic expression with the exception of an expression
that results in a divide-by-zero.

example: 0 = 0 * (sum the remaining numbers)
0 = 0 * (95 + 2 + 100 + 1/4 + 395 + 1  + 9)
0 = 0 * (               n                 )

error:  0 = 0 * (95 + 100 + 1/4 + 395) / (sqrt(9) - 2 - 1)
0 = 0 * (          n         ) / (   3    - 2 - 1)
0 = 0 * n / 0
0 = 0 / 0
divide-by-zero is an error
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 12 August 2007 This work is licensed under a Creative Commons Attribution 3.0 United States License.