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<WRAP><color red><fs 200%>Corning Community College</fs></color></WRAP>
<WRAP><fs 150%>CSCS2330 Discrete Structures</fs></WRAP>
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======Project: WEEKLY PUZZLE FUN (wpf7)======

=====Part 1: 7x7 medium-level difficulty logic-grid puzzle=====

====Objective====
To apply your skills in the solving of a logic puzzle. We've now been through the gamut of resolutions on easy difficulty. You'll find the clues may reveal less direct things, but indirectly is where the connections will be made.

====Grid-Based Puzzle Strategies====
Some things to keep in mind when solving this type of puzzle:
  * no selection in any category can be used more than once
  * analyzing what is **NOT** possible can be just as helpful as finding what **IS** possible
  * be mindful of the properties of your basic logical connective words:
    * **NOT**: typically stating an invalidation
    * **AND**: identifying a grouping (bread AND butter, indicating the two are paired in some fashion of consideration)
    * **OR**: for the purposes of these puzzles, the association of various items with the **OR** connective is typically done in an **EXCLUSIVE** fashion versus the **INCLUSIVE** fashion it can also be used as. An **EXCLUSIVE OR** (XOR) means ONE or the OTHER, but **NOT BOTH**
  * Mark off disproven cells with an **X**
  * For proven cells, some sort of confirmation mark (I like using a small solid circle)
  * Some print out the puzzle and complete it in pencil; others load the image into some sort of image/paint program and use the "fill" tool (with two different colors queued up) to complete the puzzle. Either way, you will want to record your resulting associations to report to the submit tool
  * From experience, especially with any new or less familiar activity, the more manual you make the process and perform it **by hand**, the more improvement you will reap over time
  * Be sure to cross-reference! Sometimes you'll get "half" or indirect clues in one category, which can be linked to an associated "half" or indirect clue in another category, enabling further cell eliminations or even derivations of confirmed association(s)
  * Be aware of your units, and how they progress; provided clues will often play off the patterned ordering of the units
  * Once you have fully exhausted a clue, cross it out to aid you in focusing on the clues that still need resolution

Remember, keeping track of what has been eliminated is just as important as tracking what has been identified. A lot of trouble or "dead ends" have emerged when people were not keeping full inventory on grid box eliminations.

Please do endeavor to put forth original, honest effort in the solving of these puzzles, by hand; the process will help foster and solidify many analytical reasoning skills that will influence and improve your logic and programming skills. Improvements won't happen overnight, but through consistent practice, by the end of the semester you should start reaping the benefits of such an activity.

====Puzzle Backstory====
Barry's Deli has a bunch of orders to fill.

====Puzzle====

{{ :haas:fall2017:discrete:projects:wpf7.png |}}

====Clues====

  - Omar's order costs $7.75.
  - Ronda's order is either the sandwich with bologna or the order with roast beef.
  - The order with roast beef costs less than the order with salami.
  - Neither the $7.75 sandwich nor Greg's sandwich is the order with muenster cheese.
  - Of the sandwich with salami and the sandwich with havarti cheese, one is Ronda's and the other costs $6.75.
  - The order with salami includes gouda cheese.
  - The order with provolone cheese costs less than the order with roast beef.
  - Yolanda's order doesn't include ham.
  - Ronda's order costs $8.75.
  - Of the sandwich with muenster cheese and Verna's order, one includes prosciutto and the other costs $2.75.
  - Of the $2.75 sandwich and the order with ham, one is Kenneth's and the other includes cheddar cheese.
  - The order with liverwurst costs 3 dollars more than the order with cheddar cheese.
  - The sandwich with colby jack cheese, Greg's sandwich, the sandwich with gouda cheese and the sandwich with ham are all different sandwiches.

=====Part 2: Letter Division Puzzle=====

====Objective====
Logic grids are not the only form of logic puzzle; here is another one that relies heavily on logic and reasoning in order to sift through.

A letter division puzzle is one where the numbers 0-9 have been replaced with various letters of the alphabet; it is your task to determine what number each letter maps to, and report that to me in the project submission.

====Letter Division Puzzle Strategies====
Some things to keep in mind when solving this type of puzzle:
  * take copious notes
  * jot down patterns and observations
  * perform tests to prove or disprove a relationship
  * look for any "obvious" giveaway clues, like what letters could represent 0, 1, and 9
  * try to identify the non-borrows, borrows, and "double" borrows, marking them as appropriate
  * write out relationships so that you can keep track of them, things like:
    * <nowiki>A < B << C</nowiki>
      * I use the single less than to denote a direct neighbor (A is one less than B), and the double less than sign to denote general less than-ness (we know that B is less than C, but we do not know how much it is less than C).
  * use "process of elimination" number sets
    * I will also write out each letter and all the numbers it could be, erasing eliminated values along the way. Sometimes you will arrive at an association through this method.
    * For example:
      * A = { 0 1 2 3 4 5 6 7 8 9 }
      * B = { 0 1 2 3 4 5 6 7 8 9 }
        * and so on for each letter. If we were to determine that B is not 9, erase it from B's number set. That way, when we're hunting for possible candidates for 9 (for example), we can directly rule out B
  * sometimes you can derive important clues from the multiplication aspect of the puzzle (especially finding the occasional dead-ringer for 0 or 1)
  * don't rely on just one method: use all of these methods. With different puzzles you will find differing levels of values with each method (but in general, I find the more methods I use the easier the overall puzzle becomes)

As I said: For this sort of problem, you will likely want to take notes; all the various little tests you concoct to prove or disprove some relationship can be important in the bigger picture. This may also take a bit longer and seem more overwhelming (especially at first), but really, it is just longhand math :) Remember to attack the problem in pieces, and not head-on all-at-once.

Practice some similar math problems to derive patterns so that the seemingly unfamiliar letters performing math can start to make more sense.

====Puzzle====

<code>
              LACK
        +---------
  SKILL | MISCASTS
         -SKILL
          =====
          LATALS
         -LBHKAA
          ======
           LTIHCT
          -LMKLCC
           ======
            ACTBSS
           -ALTTKK
            ======
             LHALL
</code>

^ number ^  0  ^  1  ^  2  ^  3  ^  4  ^  5  ^  6  ^  7  ^  8  ^  9  |
| letter |  |  |  |  |  |  |  |  |  |  |

=====Part 3: Easy Sudoku puzzle=====

====Objective====

With the logic grids you put your logic skills to the test, with the word math you math skills. Here, we will explore various other types of puzzles, often combining both logic and math skills to solve, but also exercising different aspects of your deduction/induction skills.

====Puzzle====

|     |  8  |     ^ |  4  |  1  |     ^ |  6  |     |  5  |
|     |     |     ^ |  2  |  6  |     ^ |     |     |     |
|  6  |     |     ^ |  7  |     |     ^ |  3  |     |  8  |
^     ^     ^     ^ ^     ^     ^     ^ ^     ^     ^     |
|  4  |  5  |     ^ |  9  |     |     ^ |     |     |  7  |
|     |  6  |  2  ^ |     |  8  |     ^ |  1  |  3  |     |
|  8  |     |     ^ |     |     |  4  ^ |     |  5  |  2  |
^     ^     ^     ^ ^     ^     ^     ^ ^     ^     ^     |
|  5  |     |  4  ^ |     |     |  6  ^ |     |     |  1  |
|     |     |     ^ |     |  4  |  2  ^ |     |     |     |
|  2  |     |  8  ^ |     |  9  |  5  ^ |     |  7  |     |

Enter numbers into the blank spaces so that each row, column and 3x3 box contains the full sequence of numbers 1 to 9.

Top row:

^  pos #0  ^  pos #1  ^  pos #2  ^  pos #3  ^  pos #4  ^  pos #5  ^  pos #6  ^  pos #7  ^  pos #8  |  
|     |  8  |     |  4  |  1  |     |  6  |     |  5  |

=====Submission=====

To submit this weekly puzzle, simply run the **submit** line below; a submit-time questionnaire will collect your puzzle results.

====Submit Tool Usage====
When you have completed work on the project, and are ready to submit, you would do the following:

<cli>
lab46:~/src/discrete/wpf$ submit discrete wpf7
Submitting discrete project "wpf7":

SUCCESSFULLY SUBMITTED
lab46:~/src/discrete/wpf$ 
</cli>
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