Go, dog! Mystery Cache

Difficulty:
2.5 out of 5
Terrain:
2.5 out of 5

Size: Size: small (small)

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Geocache Description:

NOTE: This cache is not at the posted coordinates. The cache is not in Moraine Hills State Park. This is an offset cache. In order to find the cache, you will have to perform a projection.

Do not go to the posted coordinates. Instead project a waypoint that is X meters away from those coordinates at a bearing of AB degrees 0C' 0.DE" true. At that spot you will find a micro containing the amounts to add to, or subtract from, the projected coordinates in order to locate the final. The final cache is a Small size container a short distance away from that projected location.

  • X is a palindrome and is the product of K, R, G, and M.

  • AB is a two digit number that is the seventh triangular number. AB is also the second perfect number.

  • C is the number on the card called "the Curse of Scotland." It is also the digit that repeats in decimal places 762 through 767 of pi.

  • DE is a two-digit number that is the line number for Cypora Gross on Schindler's List. DE is also the number of planar 6-hexes that exist.

  • K is the only even prime number. K is also the number of candles put on a windowsill on Independence Day in Finland.

  • R is the number of concertos for violin written by Shostakovich. R is also the first of the seven known magic numbers in nuclear physics.

  • G is the number of sides on the Canadian currency known as the "loonie." G is also the only number appearing in the titles for the tracks on the album Sailing the Seas of Cheese by the band Primus.

  • M is the only two-digit number whose digits are reversed when written in hexadecimal. M is also the number that Herbie the Love Bug used when racing.

Parking From the projected coordinates, subtract .093 from North and add .088 to West for a parking spot.

If that gives you enough information then read no further. Go find this cache.





Projections Explained
If you are not familiar with the concept of a projection, then this cache will provide you with a pleasant introduction.

A "projection" in this context means a computation that takes a (1) starting point, (2) a distance, and a (3) direction and produces a new location. Your task is to use those three pieces of information to "project" a new location. A simple example will illustrate:

Example Let us suppose that you are standing at the intersection of State and Madison in the great city of Chicago. You are looking for a pot of gold and you are told to travel one block west. So, your projected location would be the intersection of Dearborn and Madison.

In our example, we were given the starting point (State and Madison), the distance (1 block), and the direction (west). From these three pieces of information, we were able to determine the location of the pot of gold (projected location).

If the prize at the new location were not so big as a pot of gold (maybe just a gold coin), then we might like to be a little more precise in the information that we provide. For the starting location, we might like to give the coordinates. For the distance, we might choose a smaller unit of measure like feet or meters. And for the direction, we might choose to give a bearing (270 degrees in this case).

Modifying our previous example, we could direct the seeker to the coin of gold by suggesting that they start at N 41 52' 55.5" W 87 37' 40.95" and travel a distance of 124 meters at a bearing of 256 degrees 31' 36.76" (that bearing is just over 13 degrees south of due west). They would still end up at Dearborn and Madison but they would have a much better idea of precisely where at that intersection they should look for the coin of gold.

Resources
"Bearing" is a term that is new for some people. That term is perhaps best explained at the following link: Bearing tutorial.

There are a number of ways that one can perform a projection with great precision. One way is with a nifty program called FizzyCalc which is a free program created by they dynamic geocacher, fizzymagic. If you choose to use his program, you might find this FizzyCalc projection tutorial handy to have while you work.

A website which contains a very accurate a tool for projections is Geoscience Australia. If you choose to use this link, you may find these notes helpful.

Most GPS receivers perform projections. However, receivers vary in the precision available for projections. It is not certain that your GPS receiver will perform projections with the precision needed for this cache. You can, of course, use any model of receiver to hunt the cache; but getting accurate coordinates for the projected location from your GPS unit might be an issue. See the manual of your receiver for instructions.


Sample With Solution
Armed with one of these tools, try the sample problem below.

Starting at N 42 18.869' W 88 13.511', project a location that is 19082 meters away at a bearing of 339 degrees 10' 42.3"

You should get a result quite close to N 42 28.501' W 88 18.460' which is the same as N 42 28' 30.06" W 88 18' 27.6".

Happy hunting!

If you would like to know if your solution (to the puzzle, not the sample!) is within 3 meters, you can use the link below. If your solution is within 3 meters, the link also includes parking advice.

20180906: Changed size from Regular to Small. Updated description accordingly. Added "Takes < 1 hr" and "< 1 km" attributes.

Additional Hints (No hints available.)



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