This cache is NOT at the posted coordinates,
solve the puzzle below to find the corrected coordinates.
See Cryptogram University Series 101 CUS 101: Cryptogram Basics for more information on cryptography and this cache series.
CUS 107: Base Codes will teach you about positional numeral systems. Base codes are technically not a code and from a puzzle solver’s perspective could best be described as a type of substitution cipher, but they are really just other types of numeral systems. This course will go over several of those different base numeral systems, explain the basics of how they are developed and solved. Some of these base codes you will be very familiar with (Base-10 or Decimal), others you will be somewhat familiar with (Base-2 or Binary), and most which you will never have heard of before.
Base-10 (Decimal)
Base-10 (Decimal) is the system used almost universally today around the world, using ten digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is the numeral system we all know, learned in school, and use on a daily basis for counting, math, and science. The coordinates we all know and love are written using the Base-10 Decimal system on GC.com and on our GPSr/phone. Coordinates written in the Base-10 Decimal system would be a normal set of “unencrypted” coordinates.
Base-2 (Binary)
In Base-2 (Binary) only two digits are used – 0 and 1. Computers use binary primary because it aligns well with the physical nature of electrical signals and the simple off (0) and on (1) states of electronic components. The fundamental building blocks of computers, transistors, act as electronic switches, allowing or blocking the flow of current. This on/off behavior directly translates to the 0 and 1 values in binary allowing computers to process everything from numbers to text, images, sounds, and other types of data. Everything computers do is based on this binary code of 1s and 0s.
Positional Numeral Systems
When I first learned about base codes and positional numeral systems, it quite frankly blew my mind that different numeral systems existed, which could totally change the meaning behind many common numbers we frequently use in daily life without even knowing about the existence of other systems. In a positional numeral system, the base is the number of unique digits, including the digit zero, used to represent numbers.
Now for the mind-blowing part…Base-10, our decimal system, is the only one where 10 equals the number ten. The number ten is actually written ten different ways in Base positional numeral systems (see the light-yellow row in Figure 1 below). A few examples:
- 1010 is the number ten in Base-2 Binary (that only uses 1 and 0)
- 22 is the number ten in Base-4 Quaternary (that only uses the numerals 0-3)
- A is the number ten in Base-12 Duodecimal (that uses the numerals 0-9 plus A and B)
The first known use of a positional numeral system was in Ancient Babylon over 4,000 years ago in about 2,500 BC, where they developed a Base-60 numeral system using powers of 60. Interestingly, the Babylonians had no numeral for zero. The Ancient Mesoamericans (e.g. Mayans and Aztecs) in the Pre-Columbian Era (before 1492) developed a Base-20 numeral system using powers of 20. Our Base-10 Decimal system was first used in the Ancient Mediterranean (Egypt and Greece) and was believed to have originated as a result of counting on our ten fingers. Today, Base-10 Decimal is universally used around the world.
Below is a table of the most common Base positional numeral systems with our Base-10 Decimal column highlighted in bright yellow for quick and easy comparison (Figure 1). You will also see how the positional numeral systems work in the table. Essentially, the systems uses only the number of numerals listed in the Base, and that includes 0. Once you run out of single-digit numerals in that system, you go to the two-digit numeral 10 and continue, but only using that Base number of numerals.
Figure 1: Base Code Table
A cue to recognizing Base numeral systems is if you see characters that remain under a certain number. For example, if only the numerals 0-4 are used, then you are likely looking at a Base-5 Quinary number system and can solve it from there. This doesn’t always work, since you could just happen to have numbers lower than that for all the coordinates, but the chances of that are relatively low.
The CUS 107 Exam:
Solve the base code puzzle below to find the correct coordinates.
N 51° 112.1440 W 136° 51.1631