Puzzlers Lesson ​4: Coordinates Mystery Cache

A lesson on how to use the numbers you get from a puzzle Some instruction followed by an exercise for the reader.

Introduction

This is the fourth in my series of caches meant to teach people some ways to solve puzzle caches. Please read the information above the line in Puzzlers Lesson 1: Alphabets. This lesson will teach you about the type of numbers that you are looking for in the puzzle and how to use them.

Coordinates on the Earth

The earth is an oblated sphere, a ball that is slightly wider measured through the center at the equator than measured from pole to pole. That's more information than you need, so for the remainder of this cache I will just refer to the earth as a sphere (ball).

The earth rotates, like a top, giving us day and night. The line through which it rotates is called the axis. Where this axis touches the surface of the earth are the North and South Poles. The line that is half way between these these two poles is called the equator.

The equator divides the earth into two hemispheres (half-spheres), Northern and Southern Hemispheres. The equator is 0°. Each pole is 90°, north or south. Latitude measures angles between these locations.

Longitude measures the other direction. Unlike latitude, there is no natural place to draw the line from pole to pole and designate it as 0°, also called the Prime Meridian. Through much disputation and negotiation the line was finally drawn through Greenwich, a district of London, England.

The line on the opposite side of the earth is called the anti-meridian. This line is both 180° east and 180° west. The anti-meridian crosses very little land, for its length. Together, the Prime Meridian and anti-meridian divide the earth into Eastern and Western Hemispheres. Nevertheless, some refer to Eastern and Western Hemispheres as being divided by the Atlantic and Pacific Oceans, but I won't use that definition here.

Most coordinates are given in WGS-84 datum. This is the latitude and longitude datum used by default by Global Positioning System (GPS) receivers. Most allow you to switch to another datum. All these lessons will use the WGS-84 datum, unless otherwise specified. I think that any puzzle not using WGS-84 datum should give you the datum or greatly hint at what datum you should use.

Coordinate Formats

Latitude and longitude are measured in degrees, indicated with the ° symbol. Degrees are divided into minutes, with 60 minutes per degree, indicated by ' symbol. Minutes are divided into seconds, with 60 seconds per minute indicated by " symbol.

The posted (not actual) coordinates for this cache are N 41.25833° W 112.00000° specified with degrees and fractional degrees. There are 15 digits, individual characters representing numbers, when specified this way.

The posted (not actual) coordinates for this cache are N 41° 15.500' W 112° 00.000' specified in degrees, minutes and fractional minutes. There are 15 digits when coordinates are specified this way. This is the way that coordinates are usually shown on geocaching web sites.

The posted (not actual) coordinates for this cache are N 41° 15' 30.00" W 112° 00' 00.00" specified in degrees, minutes, seconds and fractional seconds. There are 17 digits when coordinates are specified this way. If you take off one digit of accuracy from the end of each then there are 15 digits.

Something that you (probably) already know is that your GPS (Global Positioning System) receiver is usually accurate to about 20 feet. Something else that you should learn is that the coordinates given are usually more accurate than this. The distance between lines of latitude are the same no matter the longitude. However, the lines of longitude get closer together as you approach the poles. Here are the accuracies for the right-most digit for each of these formats, rounded to the nearest 0.1 of each unit:

For this table the accuracy of the longitude is given at the latitude of the posted coordinates of this cache.

What to Look for in Puzzles

So, you can see that most coordinates are given with more accuracy than you can actually get with your GPSr. Don't worry about this. Just worry about getting the coordinates that you are supposed to get for the puzzle given.

Since all of the above formats can be specified by 15 (and one by 17) digits, how are you supposed to figure out which format it is in? For one thing, the placement guidelines for mystery/puzzle caches specify, "Final coordinates must be less than 2 miles (3.2 km) from the posted coordinates." (NOTE added 26 December 2017: Shortly after the ALOHA series was created in late 2011 the above limit was imposed.) As a rule of thumb that means that the actual coordinates are within two minutes of latitude or longitude. Here are the actual values, rounded to the accuracy of the given format:

For this table the difference between longitude for 2 miles is given at the latitude of the posted coordinates of this cache.

However, a cache owner may only provide part of the cache coordinates. This may be just the lowest three, four or five digits of each of the north and west coordinates. So, if you see 6, 8 or 10 parts to the puzzle then you (usually) have partial coordinates. You replace the lowest digits that you get from the puzzle with the ones that you got. But remember what you've seen in previous lessons, one letter can give two digits.

A curve ball that you may see in puzzles are 12, 16, 20 or 30 parts to the puzzle. Note that these are twice the above numbers with 30 being twice 15 (the most common number of digits in coordinates). This usually indicates that pairs of parts of the puzzle are probably used to calculate a each digit. There may also be 3 or 4 parts that are used to calculate each digit. But just because you get a multiple of one of these numbers doesn't mean that you do the above, but this is certainly one thing to try. Always remember that these are generalities because I've made puzzles where the result is 7 digits, but it is obvious where the 3 and 4 digits go.

If you have 10 digits then the first of each group of 5 will probably be the same as in the posted coordinates. The advantage of this is that you can (usually) use that first digit of each group to figure out how to decode the puzzle. However, if the minutes are near where the upper digit may change then it may be the other digit. I chose this location to demonstrate this principle. For this puzzle the degrees for west are very near the line so the minutes for this puzzle could be 58, 59, 00, 01 or 02.

Also, it is considered fair to leave out zeroes when it should be obvious where the zeroes are. So, if the puzzle were to result in the 8 digits 41155112 then they may be the lowest 4 digits of each part of the coordinates, or they may be the posted coordinates N 41° 15.500' W 112° 00.000'. It should be obvious which of the two it is, be close so that you can reasonably go to both, or there is some way to verify the coordinates.

Most people give some web site that will check and verify your coordinates, as I have below. Others will give a checksum. Unless otherwise specified, this means that you add up all of the digits and get a number. So, for instance, the checksum for N 41° 15.500' W 112° 00.000' is 4 + 1 + 1 + 5 + 5 + 0 + 0 + 1 + 1 + 2 + 0 + 0 + 0 + 0 + 0 = 20.

When zeroes are left out they are usually left out of complete coordinates. That way you have a 111 or 112 to start the west coordinates to separate the parts. So, if the results of the puzzle at these posted coordinates give you 15515599 you could rightly conclude that the actual coordinates are N 41° 15.515' W 111° 59.900' or N 41° 11.551' W 112° 00.599' because N 41° 11.551' W 111° 55.599' and N 41° 11.551' W 112° 05.599' are both too far away. Note that the zeroes were left out at the beginning or end of the minutes portion but not both. This will probably be the case for others, but watch out for when it isn't.

Also, look for the case where the cache owner has swapped the north and west coordinates. I've done this on some of my own puzzles, but I've provided enough digits for people to figure this out.

12 September 2019:
How to Convert Lat Long in DMS to Decimal Degrees in Excel
Converting Long/Lat Decimal Degrees to Degree Minute Seconds

Universal Transverse Mercator

One more way of specifying coordinates in numbers is the Universal Transverse Mercator (UTM) coordinate system. If you look just under the degrees-minutes coordinate for this cache you'll see the UTM coordinates. You should learn to recognize this type of coordinate because they may be the result of the puzzle. You don't want to miss a solve because you don't recognize them.

The posted coordinates for this cache are 12T E 416227 N 4567917. The 12T indicates a grid square. The center of each grid square is designated as 500000 easting to avoid negative numbers. The northing is measured from the southernmost line of the grid. So the given coordinates are approximately 83773 meters west from the center of the grid and approximately 4567917 meters from the southernmost line of the grid. I use "approximately" because there is inherent distortion when putting a portion of a curved surface (like part of the earth's sphere) onto a flat map.

2 miles is 3218.7 meters. This means that if the coordinates are in UTM then they can only vary from the posted coordinates by approximately this many meters. (See "approximately" above.) This means that (usually) only the lowest 4 or 5 digits will vary from the posted UTM coordinates.

Since UTM is used so infrequently used then a cache owner should probably provide all 13 digits after the 12T when specifying UTM. However, a cache owner may also make the two parts the same length giving 12 digits, or use the 12 in the puzzle and you will have 15 digits. If fewer digits are specified then use the other techniques above to figure out what to do. So, the posted coordinates for this cache may be 124162274567917, 4162274567917, 416227567917 or some other number of digits.

Puzzle

Using the information about coordinates above and information from previous puzzles, solve this puzzle:

QUIZZIFY QUAINT EASEL EDGY CANNOT SNATCH AN EAST VICTORY

You can validate your puzzle solution with certitude.

I will add a hint to solve this puzzle in one month from when this cache is published.

Update 12 November 2016: There is a hint already given in the text description above. This is something that I'll always do in my puzzles, but not everyone will give such a hint. However, as I've done here, the hint is not so obvious.

Additional hint is rot-13 encoded so that you have one more chance to figure it out without this hint: Gur chmmyr vf va jbeqf fb lbh jvyy arrq gb svaq gur inyhr bs rnpu jbeq. Gb qb guvf lbh jvyy arrq gb fhz (nf va gur purpxfhz uvag nobir) gur inyhr bs rnpu yrggre bs gur jbeq. Lbh'yy gura unir gur ahzoref gung lbh arrq gb nccyl gur yrffbaf bs guvf pnpur.

Congratulations to UsLaynes for first-to-find.