These equations will generate a series of coordinates that will eventually converge to a single value. It's possible to solve these equations with patient use of a simple scientific calculator (usually included with your computer). Note these COSine functions assume input in DEGrees, not RADians - so set your calculator or convert accordingly (degrees = 180/pi radians).
![[1] Lat = Cos(500(Long+0.3217315))/8 + Cos(5000(Long+0.3217315))/50 – 37.0201672, [2] Long = Cos(500(Lat+0.0451672))/4 + Cos(5000(Lat+0.0451672))/50 + 174.5982685](https://s3.amazonaws.com/gs-geo-images/219929a0-65da-4790-8b48-ae3cc4522fbc_l.jpg)
The ball starts rolling with an initial Longitude value, Long0. The Latitude is calculated from equation [1], using the Longitude value. The next Longitude in the sequence is given by equation [2], using that Latitude value. In an iterative process, you then calculate another Latitude and Longitude starting with the new Longitude value. Eventually the Latitude and Longitude values will not change, and this will give the position of the cache.
The seed is Long0 = 174.7962685
The cache is a 1.3 litre container painted green.
You can check your answers for this puzzle on Geochecker.com.