GC2Z81G - We Made It To #1000 !!!
By: robgreene
1. Here is the puzzle:
To solve the 'We made it to #1000!' puzzle, I found it easier to ignore the Wikipedia page, and instead focus on the instructions.
Geocache Description:
A seven-segment display, or seven-segment indicator, is a form of electronic device used for displaying decimal numerals... Seven-segment displays are widely used in digital clocks, electronic meters, and other electronic devices for displaying numerical information.
In this puzzle, the controls for the segment have gotten all jumbled up! Instead of using the widely published information on how to decode the display number, it will have to be decoded all by itself! Fortunately, the enclosed diagram illustrates how to decode the message. Note that there are 7 segments (letters "B" through "H") and one decimal point (letter "A"). Comparing them to the wikipedia page, you will also note that the letters have, indeed, been jumbled up.
The coordinates have been encoded in a hexidecimal byte -- each bit of that byte indicates if the segment is lit (a value of 1) or unlit (a value of 0). The segment values are stored in ABCD EFGH order in the byte (that is, A has the highest value and H is the 1's position).
This geocache can be found at: N 6A 6A 7C BE 32 1F 7A W 77 7F 7A 3E FF 7D 6A 7A.
2. Analyze the puzzle.
The Wikipedia page explains in detail what a G-A 7-segment display looks like, and makes mention that if a decimal is used, one should add an 8th segment. This is an 8 segment puzzle.
Wikipedia entry on 7-segment display
Here's what that means in a nutshell. Each of the 8 segments you see in the puzzle, A - H, have two states - ON or OFF. That means there are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 possible combinations. Coincidentally, there are 256 unique 2-digit numbers in the hexadecimal series, from 00 through FF.
Let's break that down to simpler language. In the Base 10 Decimal (our 'normal' numbering system) we have 10 different characters that can be used as numbers, from 0 through 9. A single digit number, therefore, can only represent 10 different unique values. If two numbers are used, each digit can have 10 different values, so there are 10 x 10 = 100 different possibilities. (Remember that 00 is a valid possibility.)
With Base 12 Hexadecimal counting, there are 16 unique characters which can be used: the numbers 0 through 9, then the letters 'a' through 'f'. A single character can therefore represent any of 16 values, and if two digits are used, there are 16 x 16 = 256 possible unique values represented. Each Hexidecimal 2-digit value, therefore, can be used to describe one possible state for all 8 segments in the 8-segment display.
3. Puzzle solution.
This puzzle can be solved by using an Excel spreadsheet and a Hexadecimal to Binary Code Converter.
Start by making a grid where the first column has a heading of 'HEX, and the next eight columns are labeled 'A', 'B', 'C', 'D', 'E', 'F', 'G', and 'H'. then, under the 'HEX' column, write the values you're looking for, according to the puzzle. It should start out looking like this:
Start by making a grid where the first column has a heading of 'HEX, and the next eight columns are labeled 'A', 'B', 'C', 'D', 'E', 'F', 'G', and 'H'. then, under the 'HEX' column, write the values you're looking for, according to the puzzle. It should start out looking like this:
The puzzle instructions clearly state that you should put the 'H' in the 'Ones' position, and the 'A" in the column with the highest value. That is why the columns are labeled A to H, not H through A.
The Wikipedia page tells you that for each hexadecimal value, the individual segments of the display should either be turned 'ON' or 'OFF'. Since the state of each segment is either 'ON' or 'OFF', you can conclude that this is a Binary Display.
Use a Base Converter to convert the Hexadecimal Numbers to Binary Numbers, being sure to add leading zeroes to the left side, if necessary, to get you to 8 characters.
For hexadecimal number 6A, the binary equivalent is 01101010. Place the binary numbers in the row next to the 6A, and in every row where you have a 6A as the clue.
Then use the converter to find the binary equivalent of the hexadecimal number 7C, which is 01111100. Place this binary equivalent in the row next to 7C.
Continue converting from hexadecimal to binary, and filling in numbers, until the whole grid has been completed.
Finally, for each Hexadecimal code number, note which of the binary segments are turned 'ON'.
Now start filling in the coordinates.
N 6A 6A 7C BE 32 1F 7A, W 77 7F 7A 3E FF 7D 6A 7A
N 4 4 7C BE 32 1F 7A, W 77 7F 7A 3E FF 7D 4 7A
N 4 4 7C BE 32 1F 7A, W 77 7F 7A 3E FF 7D 4 7A
Continue decoding until you have all the coordinate digits, as follows:
- 6A = B, D, E, G = 4
- 7C = B, C, D, E, F = 5
- BE = A, C, D, E, F, G = .3
- 32 = C, D, G = 7
- 1F = D, E, F, G, H = 2
- 7A = B, C, D, E, G = 9
- 77 = B, C, D, F, G, H = 0
- 7F = B, C, D, E, F, G, H = 8
- 3E = C, D, E, F, G = 3
- FF = A, B, C, D, E, F, G, H = .8
- 7D = B, C, D, E, F, H = 6
4. Put together the solved coordinates.
Insert the decoded numbers into the puzzle to get your solved coordinates.
- 6A = B, D, E, G = 4
- 7C = B, C, D, E, F = 5
- BE = A, C, D, E, F, G = 3.
- 32 = C, D, G = 7
- 1F = D, E, F, G, H = 2
- 7A = B, C, D, E, G = 9
- 77 = B, C, D, F, G, H = 0
- 7F = B, C, D, E, F, G, H = 8
- 3E = C, D, E, F, G = 3
- FF = A, B, C, D, E, F, G, H = 8.
- 7D = B, C, D, E, F, H = 6
5. Solved coordinates
N 44 53.729, W 089 38.649
6. Verify your solved coordinates with GeoChecker.
GeoChecker - We Made It To #1000 !!!
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