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======pctX tips and tricks======

NOTE: This document attempts to be generic to the entire range of pctX projects. Please substitute the particular number in place of X. For example, if working on **pct1**, for all references of **pctX**, use **pct1** instead.

=====How to access the puzzle in the public directory=====
From a lab46 prompt, change to the c4eng public directory, which is in **/var/public/fall2019/c4eng/**:

<cli>
lab46:~$ cd /var/public/fall2019/c4eng
lab46:/var/public/fall2019/c4eng$ 
</cli>

Next, change into the directory of the pertinent pctX project:

<cli>
lab46:/var/public/fall2019/c4eng$ cd pctX
lab46:/var/public/fall2019/c4eng/pctX$ 
</cli>

Run **ls**, you should see a list of directories named after the users in the class. Your username should be among them. Change into that directory:

<cli>
lab46:/var/public/fall2019/c4eng/pctX$ cd username
lab46:/var/public/fall2019/c4eng/pctX/username$ 
</cli>

Run **ls** again, you should see a file named **puzzle**. Display this using the **cat** command (which we are using as a text viewer):

<cli>
lab46:/var/public/fall2019/c4eng/pctX/username$ cat puzzle
</cli>

=====How do I create a project folder and the files needed for project submission?=====

First, log into lab46.

===Create the pctX project directory===
Again, where 'X' is the number of the current pct project:

<cli>
lab46:~$ mkdir -p src/c4eng/pctX
lab46:~$ 
</cli>

===Change into the new directory===

<cli>
lab46:~$ cd src/c4eng/pctX
lab46:~/src/c4eng/pctX$ 
</cli>

===Create the key file===
Let us assume your puzzle key is

<code>
    0    R
    1    B
    2    V
    3    G
    4    P
    5    M
    6    O
    7    L
    8    J
    9    K
</code>

You could use nano:

<cli>
lab46:~/src/c4eng/pctX$ nano pctX.puzzle.key
*and type in RBVGPMOLJK, hit ENTER once, and save/exit*
</cli>

===Create the solution file===
Once again, using nano:

<cli>
lab46:~/src/c4eng/pctX$ nano pctX.puzzle.solution
</cli>

===Submitting===
Once you are completed with the puzzle, have the key recorded, and the solution documented, you can submit the project from this same directory:

<cli>
lab46:~/src/c4eng/pctX$ submit c4eng pctX pctX.puzzle.key pctX.puzzle.solution
</cli>
=====Positive (greater than) number certainties=====
Finding and isolating patterns amongst the operations taking place can make available to us additional paths of pursuit for solving the puzzles.

Now, we know that if the top number is greater than ONE of the values being subtracted from it, does it also reveal anything else?

<code>
 X
-Y
==
 Z
</code>

Let's say we have, from elsewhere in the puzzle, determined that Z << X, but as yet we have not established any connection between Y and X.

Can we use this to our advantage?

Yes. Take a look at these examples:

<code>
 4    4    5    9    7
-3   -1   -3   -2   -3
==   ==   ==   ==   ==
 1    3    2    7    4
</code>

As we can see here, in the small sample size of subtractions we've tried, that when the top number is greater than one of the numbers beneath it, BOTH values beneath it are less than the top number.

Now, from this approach we cannot make any determinations about how the two lower numbers relate to each other, but we can use it to fill in some gaps.

So, if we know that Z << X, we can ALSO infer that Y << X (we just don't know how Y relates to Z).

So unless we can find an example that violates this case, we can run with it as a viable approach to take in the letter division puzzles. Tell me: is there a valid combination that violates this?
=====Less than number certainties=====
Like the above, but inverted: what if we KNOW that the top number is less than one of the two numbers beneath it? Can we also infer some pattern? Let's see:

<code>
 X
-Y
==
 Z
</code>

Let's say that we KNOW, from elsewhere in the puzzle, that X << Y. Can we use that to inform us better on how X relates to Z?

Looking at some examples:

<code>
10  11  12  13  14
-6  -9  -7  -4  -8
==  ==  ==  ==  ==
 4   2   5   9   6
</code>

As we can see in the examples above, if X is less than Y, X ends up ALSO being less than Z.

So unless we can find an example that violates this case, we can run with it as a viable approach to take in the letter division puzzles. Tell me: is there a valid combination that violates this?

Remember: we are dealing with single digit values (with the exception of the top number needing to borrow), so the viable possibilities are limited.
=====These are fun, can I do more?=====
Absolutely! My letter division puzzle database can be found here:

  * http://lab46.g7n.org/~wedge/content/ltrdiv/

Do note, that I have done a few example writeups, which may offer some further insight into strategies used, along with examples of what I am looking for as far as documentation for your solutions.