This puzzle was inspired by the
Counting Scheme cache and it's also based around a fence and some math.
About the Fence
The fence forms a border along the back side of a shopper center that runs along Coleman Avenue. The fence has end points approximately at the following two coordinate sets.
N 37° 20.483 W 121° 54.722 northwest end
N 37° 20.295 W 121° 54.194 southeast end
The fence has 300
(1) sections and each has an average length of 117.2 inches. There are 24 hollow pickets in each section, for a total of 7200 pickets over the entire length of the fence.
The cache is located at a specific number of these pickets from the northwest end of the fence. This number is TBD
(2).
About the Math
Once you find the number, the cache will be located by counting that many pickets from the northwest end of the fence. As an example if you were to determine that the number is 7100 then the cache would be located according to the following calculations.
7100 / 7200 = 0.98611111111
0.98611111111 * 300 = 295.833333333 sections from the northwest end of the fence
295 full sections + 0.833333333 sections x 24 pickets/section
295 full sections + 20 pickets
The cache would be located at the 20th picket of the 296th section from the northwest end of the fence. However, rather than counting nearly the entire length of the fence you would be better counting from the southeast end of the fence.
1 - (7100 / 7200) = 1 - 0.98611111111
0.01388888889 * 300 = 4.16666666667 sections from the southeast end of the fence
4 full sections + 0.16666666667 sections x 24 p/s
4 full sections + 4 pickets
The cache would be located at the forth picket of the fifth section from the southeast end of the fence.
If you were to determine that the number is 7300 then the cache would be located at the same forth picket of the fifth section from the southeast end of the fence. The reason for this is because the count continues back and forth between the two end points rather than starting over from one end. The picket count always begins from the northwest end of the fence but it makes more sense to reset the count from which ever end is closest.
Once you discover the number you will find the cache by simply counting out the sections and pickets or you can determine the coordinate of the cache through the use of Google Earth and calculating the total distance from the end by using the 117.2 inch per section length.
An Alternative Approach
Here's another way of finding the cache. The final waypoint of the cache, that I entered into certitude, is within three feet of the fence. As would be expected, this waypoint has a UTM coordinate set with a six digit number representing the Easting direction and a seven digit number representing the Northing direction.
10S Easting: EEEEEE Northing: NNNNNNN
If a bias of 2677 is added to the Easting number, the result is a number that will indicate the same section and picket of where the cache is located. If a bias of 5361 is subtracted from the Northing number, the result is a number that will also indicate the same section and picket of where the cache is located. Press the icon below for a more complete explanation of this approach.
About the Cache
The cache is about the size of a bison tube, well camoed and within inches of the specified picket location.
Notes
- The total number of fence sections and their average length are estimates but the puzzle is designed around them so there's no advantage for anyone to do their own survey of the fence.
- The acronym TBD means To Be Determined and in the context of this puzzle it means you need to discover this hidden number. Actually, the number is provided on this page but it's in a form that most will not recognize.