BARS::Usery Park and Lower Salt River Via Usery Road

This road sign is on northbound Usery Pass Road in (or near) Mesa, Arizona.

The road sign says...

   +-------------------------+
   | Salt River Recreation 4 |
   | Saguaro Lake Ranch    9 |
   | Saguaro Lake Marina  10 |
   | State Route 87       14 |
   +-------------------------+
   the numbers in the sign:  4  9  10  14  87

   the math is:  sqrt(87 - 14 + 10 - sqrt(4)) = 9

   more math: (14 * sqrt(4) + log(10)) * sqrt(9) = 87

   [solve for 'n']  sqrt(87 - 14 + 10 - sqrt(n)) = 9

The following documents the "history" of this BARS.

MathBabbler played with the numbers without finding any math and it was the 87 that caused him problems. Without the 87, the following arithmetic was discovered.

   14 - (10 / sqrt(4)) = 9
   14 - (10 / 2) =  9
   14 - 5 = 9

State Route 87 between Fountain Hills and Payson is also called the Beeline Highway. If only the sign said Beeline Highway instead of State Route 87, then the math would be so much easier.

Update::2006.04.11 and 2006.04.25

Playing with the numbers...

   observe... summation(4, 14) = 99
   summation(4, 14) - 10 - sqrt(9) = 86 (off-by-one)

   observe... sqrt(4) * sqrt(9) = 6 ...  6! = 720
   (sqrt(4) * sqrt(9))! / 10 + 14 = 86 (off-by-one)

   ---

   observe ... 87 = 3 * 29
   sqrt(9) = 3 ... 87 / sqrt(9) = 29

   ...the remaining numbers must evaluate to 29...

   4 + 10 + 14 = 28    (off-by-one)
   4! + 14 - 10 = 28   (off-by-one)

   observe... 14 * sqrt(4) + log(10) = 14 * 2 + 1 = 29

   got math!

   (14 * sqrt(4) + log(10)) * sqrt(9) = 87

   ...wait...

   87 - 14 = 73
   10 - sqrt(4) = 8
   73 + 8 = 81
   sqrt(81) = 9

   got more math!

   sqrt(87 - 14 + 10 - sqrt(4)) = 9

The first "got math!" solution could not be submitted to RoadSignMath.com because it used a log() function. The second "got math!" solution is valid RSM and it was submitted on 25 April 2006.


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 28 January 2006

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

AZ Hwy-87 is a great SR (State Route). Its southern terminus is near Eloy and the northern end is at Second Mesa in the Navajo Nation.

AZ Hwy-87 is Arizona Avenue when it passes through downtown Chandler.

AZ Hwy-87 between Fountain Hills and Payson is called the Beeline Highway.

North of Payson, AZ Hwy-87 goes through Pine and Strawberry to Winslow.

North of Winslow, AZ Hwy-87 goes past the Homolovi Ruins State Park and the Little Painted Desert.

AZ Hwy-387 that connects I-10 with AZ Hwy-87 south of the Valley of the Sun is a six mile scenic drive especially in the spring after heavy rains.

On the 87th day of the 2006 (Tuesday, 29 March 2006), RoadHacker will drive Arizona State Routes 87, 187, 287, 387, and 587. Arizona State Route 487 has been "decomissioned."