Binary Cache Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(small)
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There are 10 types of people in the world:
Those who understand binary, and those who don't!
This Cache is not at the listed coordinates, but is not far.
This is a simple puzzle cache where you have to use a little math,
AND CONVERT BINARY NUMBERS TO DECIMAL COORDNIATES AT THE CACHE SITE.
The binary system is a numerical system that uses only two symbols, 0 and 1. That's it.
With these two numbers you can make any number or letter we know.
Due to its ease of implementation in digital electronic circuitry using logic gates, all modern computers use the binary system internally.
| 512 |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
represents this
|
in binary is
|
|
1
|
1
|
1
|
1
|
1
|
1
|
1 |
1 |
1 |
1 |
=512+256+128+64+32+16+8+4+2+1=1023 |
(1111111111)
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|
1
|
0
|
0
|
1
|
0
|
0
|
0 |
1 |
1 |
1 |
=512+0+0+64+0+0+0+4+2+1=583
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(10001000111)
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0
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0
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0
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1
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0
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0
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1 |
0 |
1 |
1 |
=0+0+0+64+0+0+8+0+2+1=75
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(0001001011)
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BINARY NUMBERS: Here's a very simple description of binary arithmetic: Binary numbers let you use any amount you want using just TWO digits: 0 & 1.
Here are some examples:
1 in base 10 = 0001 in base 2
2 in base 10 = 0010 in base 2
3 in base 10 = 0011 in base 2
4 in base 10 = 0100 in base 2
5 in base 10 = 0101 in base 2
Each digit "1" in a binary number represents a Power of the number Two.
And each "0" represents zero:
0001 is 2 to the zero (0) power, or 1.
0010 is 2 to the 1st power, or 2.
0100 is 2 to the 2nd power, or 4 (2x2).
1000 is 2 to the 3rd power, or 8 (2x2x2).
1100 is 2 to the 3rd power + 2 to the 2nd power, or 12. (2x2x2)+(2 x 2)+(0)+(0) = 8+4+0+0=12.
1101 is 2 to the 3rd + 2 to the 2nd+(0)+2 to the zero, or 13. (2x2x2)+(2x2)+(0)+(1)=13.
The powers of 2 go something like this: 512 256 128 64 32 16 8 4 2 1
When you see a binary number like "101" or "0101" (which is the same thing), you can figure out what it is by adding the powers of 2:
0101 (binary, or base 2) = 0+4+0+1 = 5 (in base 10).
1010 (base 2) = 8+0+2+0 = 10 (base 10)
0111 (base 2) = 0+4+2+1 = 7 in base 10.
1111111111 (base 2) = 512+256+128+64+32+16+8+4+2+1 = 1023 in base 10.
BINARY ADDITION
Adding two binary numbers together is like adding decimal (base 10) numbers, except 1+1 = 10 (in binary, that is), so you have to carry the one to the next column.
0001 + 0100 = 0101 (no carries to get this).
0001 + 0001 = 0010 (1+1 is 10, carry the 1 to the next column).
0011 + 0011 = 0110 (1+1 = 10, so carry, then 1+1+1 = 11, so carry again).
0011 + 0101 = 1000 (carry in every column here).
LARGER BINARY NUMBERS
Here are the numbers from 0 to 15 (base 10) written in binary, or base 2:
0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001, 10=1010, 11=1011, 12=1100, 13=1101, 14=1110, 15=1111.
To represent larger whole numbers, you need more places in the binary number:
so, 16=10000, 17=10001. Also, 53=110101, and 756=1011110100,(or 1x512 + 0x256 + 1x128 + 1x64 + 1x32 + 1x16 + 0x8 + 1x4 + 0x2 + 0x1).
Note that 1100 (12) is the same as 001100 is the same as 000001100.
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Binary Addition The addition of binary numbers is similar to the decimal system.
The only difference is to carry over when the result is '10' (2).
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 (= 0, carry 1) = 10
For example:
Binary Decimal 10
0 1 1 0 1 (13)
+ 1 0 1 1 1 + (23)
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= 1 0 0 1 0 0 (36)
Now that we know that, the coordinates are going to be in the following format:
N A° B . C
W 0D° E . F (NOTE: the "0"(zero) just after the "W" Actually IS a "0"(zero))
HERE IS AN EXAMPLE
For North:
IF:
A= 100110 = (38)
B= 11100 = (28)
C= 110110110 = (438)
Then the North Coordinate = N 100110° 11100 . 110110110 = N 38° 28.438 (in this example).
And for West:
IF:
D= 1010001 = (81)(Remember, this is 081)
E= 11101 = (29
F= = 100110001 = (305
Then the West Coordinate = W (0)1010001° 11101 . 100110001 = W 081° 29.305, (Again, In This Example)
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Here is Another Example:
Cache coordinates in Base 10 (Decimal) and Base 2 (Binary):
N 34° 54.398 is N 100010° 110110.110001110
W 082° 18.260 is W (0) 1010010° 10010.100000100
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NOW FOR THE CACHE
When you get to the POSTED Coordinates (which are NOT the final coordinates) You will search for a hidden container that holds a strip with 2 sets of Binary Numbers (You will probably need to use EXTREME STEALTH!).
THERE IS ONE SET FOR (N) AND ONE SET FOR (W).
To get the FINAL COORDINATES YOU MUST CONVERT THE BINARY (Base 2) NUMBERS TO DECIMAL (Base 10) NUMBERS for the Coordinates, and INPUT THEM INTO YOUR GPS.(See examples above)
NOW, USING THE NEW COORDINATES, GO FIND THE CACHE!
NOTE, You do NOT need to go down ANY bank to retrieve the container at the 1st stage or the final! ALSO, you do NOT need to cross ANY Fence!!
(Permission given by Casey for this cache placement)
HAPPY CACHING!
You can check your answers for this puzzle on Geochecker.com.
Co-FTF HONORS GO TO...AgentHop and HopsGeneral!!!
Additional Hints
(Decrypt)
[Stage 1]: Haqre gur pbeare cbfg pnc (ng gur cvar)
[Stage 2], Pbeare cbfg ohg ab gerr