Millcreek became Utah's newest city on December 28, 2016. The map below shows how Millcreek is squeezed between Salt Lake City, South Salt Lake City, Taylorsville, Murray, and Holladay. It stretches from the lower slopes of Grandeur and Olympus on its east all the way to the Jordan River on its west. Regions that might otherwise have been a part of Millcreek were instead plucked away by cities that incorporated sooner. Notice in particular how Salt Lake City managed to cherry-pick Brickyard Plaza without taking in the surrounding neighborhoods. This maneuver spurred a change in the state laws governing annexations.
When solving this puzzle, you will need to know the exact boundaries of Millcreek. This interactive map will serve as the official reference for all boundary questions. You will need to zoom in to see boundary details. (For ease of use, I recommend that you turn off the zip code, city council, and zoning layers.)
Below are six photographs that I took on major streets in Millcreek. For each photograph, you must determine the exact coordinates of a specific detail. To ensure that your coordinates agree with mine, I have given you partial coordinates for each photograph. You need only fill in the blanks.
Point A (star above sign) = N 40° __ __ . __ 14' W 111° __ __ . __ 50'
Point B (lion) = N 40° __ __ . __ 90' W 111° __ __ . __ 34'
Point C (between front middle pillars) = N 40° __ __ . __ 21' W 111° __ __ . __ 70'
Point D (flagpole) = N 40° __ __ . __ 01' W 111° __ __ . __ 44'
Point E (SE corner of building) = N 40° __ __ . __ 09' W 111° __ __ . __ 62'
Point F (wrench) = N 40° __ __ . __ 01' W 111° __ __ . __ 52'
When you have points A through F, here's how to locate the cache:
- Find the point X in Millcreek so that the triangle ABX is equilateral.
- Find the point Y in Millcreek so that Y is equidistant from both C and D and is exactly 1600 meters from the posted coordinates.
- Find the point Z in Millcreek so that the angles EFZ and FEZ are both 45 degrees.
- Find the circle on which points X, Y, and Z all lie.
- Find the (infinite) line that goes through the posted coordinates and the center of the circle.
The cache is on the circle, on the line, and in Millcreek.
There are a variety of ways to solve this puzzle, but I suggest you take your inspiration from the ancient Greeks. They studied how to do the types of geometric constructions that are required by this problem using only compass (the kind that draws circles) and straightedge. To that end, here is a tool that will draw circles and lines on Google Earth.
If you're interested in solving the puzzle like the Greeks, here is a tutorial on geometric constructions. It is possible to solve the puzzle by measuring distances (with the Google Earth ruler), drawing lines and circles (with the tool I've given you), and putting (the tip of) Google Earth placemarks at intersections. For best results, be sure that you zoom *way* in when using the ruler or placing a placemark. Distances can be measured very precisely this way. (The angle measurements of the ruler, however, are too imprecise to be of use.)
No matter how you approach the problem, take the time to be precise, and have fun!