Skip to content

The Matrix Mystery Cache

Hidden : 3/17/2009
Difficulty:
4.5 out of 5
Terrain:
3.5 out of 5

Size: Size:   regular (regular)

Join now to view geocache location details. It's free!

Watch

How Geocaching Works

Please note Use of geocaching.com services is subject to the terms and conditions in our disclaimer.

Geocache Description:

How good is your knowledge of Matrices? These thing are very powerful and are used in most areas of Engineering, Physics and Mathematics. They are also used in high level cryptography algorithms to encode and decode radio transmissions. The maths is not too difficult, but understanding the theory is what will challenge you...

The above coordinates are NOT for the final location of the cache.


The following 3 x 3 matrices will provide you with the location of the cache.


[ 18 33 24 ]        [ 19 23 25 ]
[ 27 42 24 ]        [ 28 32 25 ]
[ 18 29 17 ]        [ 19 23 17 ]


Let's call these two C1 and C2

The problem is that each of the above 3 x 3 matrices have been coded with a Key Matrix. This key matrix is a single 3 x 3 matrix. Let’s call it A, and looks like this:


[ 1 3 2 ]
[ 1 3 3 ]
[ 1 2 2 ]



I know what you're thinking. I can sense your thoughts. I know that you're afraid. You're afraid of what you will discover. You're afraid of change.

I don't know the future. I didn't create this cache to tell you how this is going to end. I created this cache to tell you how it's going to begin.

I'm going to end this description and then I'm going to show you what you don't want to see. I'm going to show you a world without words, a world without rules and controls, without borders or boundaries, a world where anything is possible.


Inverse Matrix Theory will tell you that if:


A x B = C


Then:


B = Ai x C


You need to take this one step at a time. You need to start by letting C be the encrypted matrices C1 and C2 that you have been given above. You need to let B be the decrypted matrices B1 and B2 that will give you the latitude and longitude. The decrypted matrices are what you need to solve.

Now, under normal mathematical situations, if you wanted to find B, then the resulting equation would look something like this:


B = C / A

The problem is that matrices are “non-communative”, in that, division of matrices does not work. This is where the Inverse part of Inverse Matrix Theory comes in.

If Ai represents the inverse of A then:


[Ai x A] x B = Ai x C


Do you remember the classic rule with equations? The one that says that what you do to one side of the equals sign, you have to do to the other side? Well, the same applied here. One thing to note with the above equation is that the order in which you do the multiplication is important:


E x F does not equal F x E


Now, one of the results of multiplying a matrix by its inverse (Ai x A), is that you get the Identity Matrix (I). This is a really handy result because it is the same as multiplying any number by 1. So, bearing this in mind, we now have:


I x B = Ai x C


This now gives:


B = Ai x C


Now, what you should realise, and see, is that you have solved for the decrypted matrix B. For latitude, it may look something like this.


[ 0 3 3 ]
[ 0 5 3 ]
[ 7 5 3 ]


This would be read as 33° 53.753

Where you go from there is a choice I leave to you...


Location History:

Mowbray Park is the launching ground for this Mystery Cache.

Named after the adjoining Mowbray Road, Sir John Robert Mowbray (1815-1899), was an English Politician known as the “father of the House of Commons”.

The lands that define this park were acquired in three stages – in 1938 from the Lavander Estates subdivision, in 1957 from the Cumberland County Council and in 1978 from private ownership.

The park contains estuarine vegetation of Swamp She-Oaks, mangroves and rushes, combined with Sydney Sandstone gully forests of Blackbutt, Red Gum and Red Bloodwood.


Parking:

The best parking for this is at Avian Cresent (No Through Road).

Be advised that you CAN NOT turn into Avian Cresent from Mowbray Road.

Once you have parked, walk down Mowbray Road and turn down the steps.

If you want a really enjoyable walk in, enter via Avro Cresent.


Optional Cache Log requirements:

When you have been successful finding the cache, there are a pair of Nerd Glasses in the cache. Why not don them and take a photo of you with the cache and post it together with your log and tell us how much of a Nerd you are.


Please do not remove the glasses from the cache


House Keeping:

  1. Please ensure that you place the cache back exactly as you found it and reinstate the camo also.
  2. If you forgot your pen or pencil and take the one out of this cache, please say so in your log so that the Cache Owner or the next Cacher can replace it.
  3. If you intend on taking a trackable, please leave a trackable.

Additional Hints (Decrypt)

Lbh arrq gb xabj ubj gb cresbez Zngevk Zhygvcyvpngvba naq ubj gb pnyphyngr gur Vairefr bs n Zngevk. Jung? Lbh gubhtug V jnf abg tbvat gb tvir lbh nyy gur nafjref?

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)