A more appropriate name for this mystery cache might be "GeoCheck Frustration".
Binary Search: Strategy
There would not be too many who have not played the number guessing game in which we have to guess a number between two numbers and are told whether the guess is correct, higher or lower. We would also know that the most efficient strategy is to choose a middle value of the remaining possible answers at each turn.
This is the Binary Search strategy and also works for higher dimensions such as area, volume, etc.
Binary Search: The Cache
"What has all that to do with geocaching?" you say? I am glad you asked. A cache has been hidden within 500 metres of the posted coordinates. To help you narrow down the coordinates for GZ, GeoCheck has been set for guessing the coordinates to GZ.
Here's the Binary Search bit ... GeoCheck has been set to indicate whether your guess/solution is within 500 metres of GZ. If your guess is within 10 metres, you will be given the actual coordinates to GZ.
Make a guess for the coordinates of GZ
Geeky Nerdy Stuff
The area bounded by a radius of 500 m is approximately 785x103 m2. If you optimally divide the remaining area in half each iteration, it should take at most twelve attempts to narrow your search area to the equivalent of a 10 m radius. Of course, armed with your geo-experience and geoknow-how, it could take fewer attempts.
Why "GeoCheck Frustration"? If you employ the optimal search strategy, on average half your attempts will be outside the 500 m radius so GeoCheck will time you out about 6 times. You will have to just wait out the time-out. Neither this CO nor GroundSpeak accepts responsbilitiy for smashed computer displays, family members shocked by expletives, or any other cacher-induced disarrangements.
Binary Search: Near GZ
On arrival, when you are near to GZ, employ the following binary search algorithm to fine-tune your position to the cache.
Up-Down Position
• eliminate the upper half as possibility; then eliminate the lower half of the remainder as possibility; now eliminate the lower half of the remainder again; go to the lower of the two remainders
Left-Right Position
• GPS tends to bounce around due to the terrain, so you may need to search broadly.
Binary Search: Accessing the Cache
FTF honours to the Uber-Perservering Marj01, Brewmaker, EverestHigh and MaxAdventurer.