10 Coordinates Mystery Cache

The cache is not at coordinates listed. You are looking for a camouflaged lock-n-lock somewhere on or near the Microsoft campus, but to find it you need to solve for 10 coordinates.

It's been said, "There are 10 types of people in this world: those that understand binary and those that don't." If you got that joke, you might be relieved you don't have to solve for quite so many coordinates and can skip to the puzzle section below. But if you didn't get the joke, let me explain.

Education

A numeric base, or radix, is a system of positional digits. Base 10, or decimal - what we all use in basic math and speech - changes the next digit position at number 10. That is, numbers from 0 - 9 are in the first digit position and when we reach 10 we increment the second digit position. 10-99 use the first two digit positions and when we reach 100 we increment the third digit position. And so on.

Base 2, or binary, is even simpler (in terms of positional digits). 0 - 1 are the first digit, 2 increments the second digit, and 4 increments the third digit.. So counting to 4 looks like: 000, 001, 010, 011, 100. Understand the joke now?

But why binary? Consider that computers run on electricity which quickly turns off and on. Off and on are binary states: off is 0 and on is 1. So computers naturally use binary, but programmers more commonly use base 10, base 16 (hexadecimal), and occasionally base 8 (octal). (There is also base 64 commonly used in computation, but mainly as an encoding system.)

You might be wondering how we represent numbers greater than 9. Numbers greater than 9 are most often represented as letters. Hexadecimal uses 0 - 9 and A - F (case-insensitive), where A is 10, B is 11, ... F is 15. In base 64, the case of the letters does matter, so "A" is different than "a".

In computer programming languages, we typically represent different bases with notations:

• Binary, though not typically written in programming languages, is typically written as 0bd, where d is the digit(s), such that 0b1 is 1 and 0b10 is 2.
• Decimal is written as is with no additional notation.
• Octal is typically written as \ddd, such that \001 is 1 and \010 is 8.
• Hexadecimal is typically written 0xd, such that 0x1 is 1 and 0x10 is 16.

A simple mathematical formula for converting from a numeric base representation to decimal is: d₁b^n-1 + d₂b^n-2 + ... + d_nb⁰, where b(ase) > 1 and 0 ≤ d(igit)_i < b, and n is the digit position from left to right. So hexadecimal number 0x8d7, where "d" is 13, is 8 * 16² + 13 * 16¹ + 7 * 16⁰ = 2048 + 208 + 7 = 2263.

Puzzle

The degrees and minutes of the coordinates are correct. To find the fractional minutes, you need to convert the following to decimal numbers.

1. AB = 0x31
2. C = 0b11
3. DEF = \150

Use the decimal results in the longitude and latitude: N 47° 38.ABC W 122° 08.DEF. You can check your solution on GeoChecker.com.