 RAID-5 Use Your Witz
A cache by WitzAbout Hidden: 6/6/2007
Size:  (Regular) Difficulty:  Terrain:  (1 is easiest, 5 is hardest)
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This is a 4-Waypoint Puzzle Cache.
But you do not have to find all 4 in order to solve the puzzle. In
fact, you should only find 3! Also you find 3 of the coordinates in
any order you want!.
A) N 38° 55.866 W 104° 50.235
B) N 38° 54.936 W 104° 45.075
C) N 38° 56.787 W 104° 43.729
D) N 38° 58.587 W 104° 46.314
6/8/2007: Congrats to Claudey for being the
first to find the cache with the revised clues!
06-06-2007 Note! All 4 of the clues are
updated and replaced and ready to go!
The new calculated coordinates should (hopefully!) put you closer
to the cache than the old clues (it had been about 50 feet away -
you should be within 20 feet away if I did it
correctly!)
Changed hide date from original: 12/14/2005 to 6/6/2007.
I wanted to make a puzzle cache that people could find even if they
had trouble finding one of the waypoints. And it turns out, there
is a method for storing computer data that does just that: RAID-5(Wikipedia).
RAID stands for Redundant Array of Independent Disks, also known as
Redundant Array of Inexpensive Disks. To solve the puzzle for this
cache, you will learn how RAID-5 works.
Here is my version of how RAID-5 works - little did you know that
this cache had educational value!
Let's say there is a lot of data to store, and there are 4 drives
to store the data on:
There are a couple of disadvantages with this system. The first is
that if one drive goes down, 1/4th of the data is lost. Another
disadvantage is that a file usually is only on one drive, so all
the data has to come from one disk, and the other 3 are idle.
Some of the other RAID specifications deal with the speed and
others deal with storing the data redundantly. For example, RAID-0
says to stripe the data across the disks:
This means reading a file is faster, because a chunk is read from
each disk, allowing the file to be read or written more quickly.
But if 1 disk is lost, any files that have a block on failed disk
are lost.
RAID-1 says to mirror the data - so 2 copies of the data are
stored, with one drive being a complete copy of the other:
In a four disk system, that cuts the storage in half, and there is
not normally a speed advantage of being able to read from multiple
disks at once. But it is the simplest way to implement redundancy,
or 'Hot Backup' for disks (I might even make a RAID-1 cache at some
point). If one disk fails, the other disk in the mirror continues
to provide the data with no impact to the system. In systems where
a disk can be replaced without powering down the system, the system
can copy all the data back to a new drive on the fly.
RAID-5 is a compromise to give the most storage, and the best
speed, with redundancy. And versions of this are used in all sorts
of server applications.
The data is striped across the disks for performance. For example,
reading file ABC, the data comes from disk A, B and C. When the
data for ABC is written, a recovery block (shown as CRC in this
case), is written to disk D. This recovery block is used to
recreate the data if a disk fails.
Let us say for example, that disk C fails:
The system will immediately recognize that the disk has failed, and
will emulate the missing disk by calculating the missing
blocks:
So reading file ABC - block A is read from Disk A, block B is read
from disk B, and block C is calculated by reading CRC1 from disk D,
and using the data from blocks A, B & CRC1 to calculate the
data from block C.
There is a performance impact when running this way - but the
calculation is pretty fast. In the case of reading DEF, there is no
performance impact for this set of data, as it just ignores the
missing CRC2.
RAID-5 can be implemented with any number of disks, not just the 4
I've shown graphically. But the more disks you have, the more
vulnerable the system is to having a second disk fail before the
first is replaced. There are methods to deal with that such as
hot-spares (empty drives that the system can automatically mount up
if one disk fails) and variations of multiple CRC volumes. But I'm
only talking about the most straightforward version of
RAID-5.
The method used to calculate the CRC in the first case, and to
recover missing blocks when a disk fails, is called XOR - or
Exclusive-OR. This is very easy for computers to calculate:
If there is 0 and 0 or 1 and 1 coming in, there is 0 coming out. If
the bits mismatch, 1 and 0 or 0 and 1, there is a 1 coming out of
XOR.
Applying this to bytes of data, it allows the creation of a
recovery-block - also it can recover any one missing block.
In the example above, A xor B xor C = CRC1.
A xor B xor CRC1 gives the value for C.
A xor CRC1 xor C gives the value for B.
CRC1 xor B xor C gives the value for A.
And this works in any order: C xor CRC1 xor A still gives the value
for B
For this puzzle cache, I have simplified the calculations. Instead
of having to work with the encoding of characters in a block, with
8 or 16 bits per character, I have encoded this cache with 4 bits
(using only decimal numbers). And to make it even easier, I am
giving you a lookup table for the 16-by-16 possible XOR
values:
View or right-click to
download
You can look up in either order - you can start with the first
number on the top or on the left. Then use the second number with
the opposite. Meet at the grid-point, and you get the XOR value for
those 2 numbers.
In the example above, let us assign: A=3, B=6, C=9. Start
with A xor B: 3 xor 6 = 5; then take the 5 and xor it with C: 5 xor
9 = 12. The CRC1 is 12.
Solving for each missing value:
Find C: A xor B xor CRC1 = C: 3 xor 6 = 5; 5 xor 12 = 10; C =
9!
Find B: A xor CRC1 xor C = B: 3 xor 12 = 15; 15 xor 9 = 6; B =
6!
Find A: CRC1 xor B xor C: 12 xor 6 = 10; 10 xor 9 = 3; A = 3!
To find the final cache, you will have to calculate the missing
values from the failed disk (missing waypoint-clue). I am not going
to remove one of the waypoints-clues; I am going to let you decide
which waypoint to skip.
You might be tempted to find all 4 waypoints so you don't have to
calculate the missing clue. But that is breaking the rules of this
puzzle. To that end, I have done 2 things to motivate you to solve
the puzzle the correct way. First, the 4 waypoint-clues are spread
really far apart - it would take you as long or longer to go to the
fourth clue as to do the calculations. Second, I am suggesting that
you to do an additional calculation to prove you did the XOR
calculations and the proof will tell me which waypoint-clue
you skipped.
To make the calculations easier, I have created a set of worksheets
to help you calculate the location of the final cache.
Printable Worksheets on a page
Or view/print each of the four worksheets separately:
Collected and Calculated Worksheet
Missing Blocks Worksheet
Final Coordinates Worksheet
Proof Worksheet
I have also created instructions/examples to use the worksheets:
Example
In summary, you will want to:
Take a printout of the worksheet page, and a version of the
XOR 16x16 look-up matrix with you.
Pick out which 3 waypoint-clues you are going to find.
Write in the values from the 3 waypoint-clues onto the
worksheet.
Calculate the missing values, the cache coordinates, and the
proof.
Visit the cache, sign the log.
Log your visit to the cache on the geocaching.com
site.
Optionally, send us an email (through
geocaching.com) with the proof value and the
waypoint-clue you skipped (A, B, C or D). And any direct
comments.
Please do not post any hint values in your
online logs - even encrypted
There are 2 First-To-Find gifts in the cache for the first 2
people/teams to find the cache. Please take only one - first FTF
get to chose. The items are of the same base value, although one
has the potential to be worth a whole lot more ;-)
Final cache solution is within the bounds of the 4 listed
Coordinates - if you calculate outside this area, try again!
:)
All the points are designed to be accessed via a
'secret' path (see also GCQP3X)
Update 6/6/2006 - I finally got the other 3 update clue markers
replaced last night. The puzzle is ready to go again. I have
decided to change the listed coordinates for this puzzle to a
nearby parking place. This means any travelbugs will get more
accurate milage.
I have reduced the difficult/terrain to 2.5/3.0 because this puzzle
is not that hard. Some people were intimidated by all the pages of
math. I have moved the sample math to a seperate web page. Note:
most people who have done this puzzle report that it is pretty
straightforward and really is worth doing the math than going after
the 4th coordinate.
Also I will add solver web page as well.
Update 3/27/2006 - included 50'NW info, updated encrypted hint,
added a little more description to end, and dropped difficulty from
3.5 to 3.0 - it comes up as a 4.0/4.0, but it isn't that hard -
also FTF prizes are gone, but there are still plenty of good trade
items!
You can check your answers for this puzzle on
Geochecker.com.
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2 user(s) watching this cache.
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