Hexadecimal Sudoku

I once wrote a puzzle book full of Hexadecimal Sudoku puzzles.  I was a bit hasty in my publication of this  book, and as a result, I had a large number of "non-linear" puzzles.  These are puzzles with more than one valid solution.  Since that time I've worked, as the question re-emerged in my mind again and again, to find a proper algorithm for detecting these divergent puzzles.

I nearly resorted to creating an " automatic puzzle solver" in Prolog as intuition tells me that it should be simple to test the puzzle as being "valid" or "invalid."  This is because Prolog is EXCEPTIONALLY good at performing logical operations (symbolic logic).  This language is a philosophy student's DREAM proof-maker.  It does "truth-trees" in nothing flat, and goal-oriented programming is very intuitive.  It may take a little "getting used to" when it comes to the syntax versus other programs, but once you're going, it does game-play, predator-prey modeling, and other AI operations quite well.

Before I invested too much time in making this program, I went back to VB where I started this application originally and started on a new algorithm for making the puzzles based on some of the examples I was seeing in the 9X9 puzzle-generating codes freely available and found that those generators were often prone to the same pitfalls mine were.  I started a few fully-random solution generator methods and was exceedingly disappointed at the 100% rate of painting themselves into corners by 60%.  BUT the traversing methods I was playing with exposed a test method (or a few) that I could use to identify the signs of non-linearity in the puzzle and thus fit it.

SO...  I've included a puzzle here and if I see quick propagation of this message then I will initiate a new blog page for Hexadecimal Sudoku Puzzles.

I'll post today's solution next week Monday.

Feel free to leave comments if you enjoy puzzles like this.

If I Could Describe my Dream-Car...

    When I was a teenager I always dreamed of designing and making my own car...  You know, like Ferruccio Lamborghini.  I had drawings, mechanical, artistic and drafting, complete with all views.  The thing is, unlike the Lamborghini, I always dreamed of an ultra-quiet, ultra-efficient, sporty looking, high performance electric or hybrid car.  Yes, I'm sure MANY people thought of making hybrids years before they made their way into our world as manufactured vehicles.  The thing is, when gas was at $1.00 / gallon there wasn't much motivation to develop such vehicles.  Today, on the other hand, I see the vehicles of my dreams being made in a way I thought I'd never see in my lifetime.

...But I digress...

    Yesterday at the SAE, Noise,Vibration & Harshness (NVH) conference in Grand Rapids, Michigan I had the pleasure of looking over an AWESOME electric car.  I highly recommend it.  I just wish I could afford one.  Here...   Have a silent walk around with me...  because it left me speechless.

Commentary on Yahoo Careers

I scanned through this Yahoo Post and had to wonder who the yahoo was that compiled their information.  Being as there was no place to leave a comment, I felt the need to then post my thoughts here.  I get the logic behind suggesting to NOT take a major in certain fields if your goal of getting the degree is to be hired into A job (regardless of personal interests).  Their suggestions, per the usual, seem to leave out some VERY relevant and important fields...  Engineering, being one of those near and dear to my heart.

There are many fields of Engineering and a great deal of need in the world for well trained engineers.  So why is it that our popular media seems to (aside from making intelligent people the butt of their jokes - i.e. The Big Bang Theory) ignore and even denounce science and engineering? 

Here is one place where I feel the NEED to make an unsolicited plug for FIRST ROBOTICS.   This is an organization that has made popular the application of science and the principles of engineering to many teenagers.  Perhaps it's finally time for our media to grow up and catch on to what's happening here in America and around the world.  FIRST is an international competition that spans the globe.  I have mentored 2 different teams in various years and I strongly encourage any professional engineer to (if they've never before) seek out a team and be a part of the movement.

Let's all make it a point to help our kids find the fun and excitement that there is in learning how the machines of today work, and in discovering and developing how machines of tomorrow WILL work.

Going back to my initial point, I think that anyone seeking to go to college should pursue what he or she LOVES, and in doing so he or she will excel in his or her chosen field.  The degree you earn has some bearing on your future, but WHAT YOU DO with that degree has a far cry greater influence on your success.

Update on the Demo Part Search

I've updated the Demo Part Search

<CLICK HERE>

I plan to have a series of images posted here this week (hopefully by 5/1) to describe the process used for that demo and images of the results.

Until then...

Plastics Classification - Chemical Classifications

Types:
 
    So, in the continuing discussion of how we classify polymers, we now need to talk about their chemical classification.  For the purposes of this blog and for the time being I will restrict the discussion of polymer chemistry to thermoplastics, and those most typically used in injection molding; although many of these are also made in specific grades meant for other processes such as Thermoforming, Extrusion, Rotational Molding, etc.
 
    Polymers, being organic compounds created via reactions of other organic monomers and reactants with 2 or more active sites on the molecule, are classified by the chemical groups that make up the repeating segments of the polymer chain.

    The following is a list of polymer chemical classes:
1) Polyolefins
2) Polystyrenes
3) Polyesters
4) Polyethers
5) Polyamides
6) Polyimides
7) Poly-Aldehydes (i.e. Polyoxymethylene - polymerized formaldehyde)
8) Poly-Acrylates


The next several blog posts will be devoted to discussing these and other various polymer chemical groups, the type of polymerization reaction involved in the making of those specific polymers, typical uses and properties for those polymers.


Common Polymerization Reactions:

Polymerization reactions include the following common processes as well as others: Linear Step, Non-Linear Step, Free Radical, Ionic, Cationic, Anionic Polymerization.

Step Polymerization - The combining of a monomer as a whole unit into chains, step-by-step.
 
    Linear step polymerization (i.e. condensation polymerization) is where a monomer will maintain it's structure but become chemically linked into chains, covalently bonded, of varying length.  Polyethylene is one example of this.  Ethane is catalyzed and the molecules link together to form longer hydrocarbon chains.  In this way, octane, heptane, decane, and other hydrocarbons might be looked at as being linked in family with polyethylene.  The term "linear" means that it will yield a thermoplastic material as there 2 and only 2 active sites on the monomer chain.

    Non-Linear Step Polymerization is essentially just like the linear except that there are 3 or more active sites on the monomer and thus a thermoset is formed.  The pint where the first side chain is formed is referenced as the "gel point."  Essentially, these lead to network polymers.

 Living  Polymerization -A Living polymer is one where there is no termination to the polymerization reaction.  These polymers can "self-heal" but the trade-off is that they're not safe for food or drug applications.

Free Radical Polymerization - The monomer has Pi-bonds (double and/or triple bonds) that are broken via the introduction of a source of free radicals.  This then opens the active sites and allows for the formation of the polymer chain and with its creation, the free radicals are recovered like a catalyst.  Typically, free radicals are introduced in the form of peroxides, and can be excited (activated) by heat or UV light.  Polystyrene is the most common example of free radical polymerization.


Ionic Polymerization - Chain polymerization that uses active centers with an ionic charge.  This is done with olyfinic monomers.  There are two types:

    Cationic Polymerization - The active centers are positively charged.  It has a defined termination process.

    Anionic Polymerization - The active centers are negatively charged.  Lacks a termination process. Instead, there is a chain transfer stage.  Polystyrene formed in liquid ammonia was one of the first applications for this process.

Ring Opening Polymerization - Polymers with a structure that looks like:  -[R-Z]n-  (the linking group is Z) can be polymerized by step polymerization.   In the case of a cyclic monomer, the ring can be broken in order to facilitate polymerization.  The primary mechanism that drives this is either the relief of bond angle strain or steric repulsions.
   
Solid State Polymerization - Polymerization of a monomer that exists in the solid and crystals are formed by adding heat or ultraviolet radiation.  These tend to yield highly oriented polymers.


Group Transfer Polymerization - Generally used for acrylic and methacrylic monomers (i.e. methacrylates - PMMA), this type of polymerization propagates by way of reacting a terminal silyl ketene acetal with some monomer by addition thus transferring the group to the monomer and creating a new terminal silyl ketene acetal group on the growing polymer.  It is initiated with monomers containing 2 or more silyl ketene acetal sites, and is catalysed by anions.



Homopolymers versus Copolymers (and Terpolymers):

    The term homopolymer refers to a polymer comprised of a single repeating monomer.  Copolymers have two different monomer links that are connected, perhaps alternating, along the polymer chain.  Examples of co-polymers include Styrene-Acrylonitrile, Butadiene-Styrene (aka High Impact Polystyrene or HIPS).

    Terpolymers are, as one might now imagine, polymers comprised of three monomer units that alternate along the polymer chain.  The most common example of a terpolymer is Acrylonitrile-Butadiene-Styrene (ABS - It's NOT the break system in your car).

Polymer Classification - Morphology

This is a continuation of the discussion started last Wednesday.  Once we determine whether our polymer is thermoplastic or thermoset, then we want to know some things about something called, "morphology."  The term morphology refers to the structure of the molecules as they make up the polymer matrix.  This is more relevant to thermoplastics, but there are some thermosets where the morphology plays a role in the properties of the resin.  The two primary morphological states of interest to us, as engineers, are crystalline and amorphous.  Well, crystalline is a relative term as polymers tend to be more "semi-crystalline" than truly crystalline the way a metal is. 

If one were to imagine a pile of sticks.  Pulling on one of the sticks will lead the puller to the conclusion that the pieces are entangled.  The same is true of amorphous materials such a polycarbonate.  The side-chains on the molecules create entanglements that help add to the strength of the polymer where crystallinity is lacking and would otherwise provide strength.  Also like the stick pile, the molecules in an amorphous material are porous on the molecular level.  This tends to make them especially susceptible to chemical attack.  Clear polymers are generally known for being especially sensitive to solvents when under stress - and more sensitive to tensile stress than compressive.  Some amorphous materials are known for being brittle (i.e. Polystyrene) while others are known for their toughness (i.e. Polycarbonate).  This is generally due to the differences in intermolecular forces (i.e. van der Waals forces). 

Some examples of amorphous materials are:  Polycarbonate, Polystyrene, Polymethylmethacrilate (PMMA - Acrylic), Acrilonitrile Alloys (SAN, ABS, etc), Polyvinylchloride (PVC), Transparent Nylon 12,  and many others.

On the other hand, if one were to imagine the image of a plate of spaghetti, we have an image that's more descriptive of a crystalline material.  The polymer chains are narrow and long.  Now if we imagine that our strands of spaghetti were made of tiny little magnetic balls, then we might get a mental image of how they would want to fold and form crystals as they cool.  When it comes to the flow of a polymer, crystalline polymers tend to align and then flow very freely past one another where amorphous polymers tend to be thicker with a less distinct fluid transition.  The morphology of crystalline polymers is affected by the shear history during flow.  The higher the shear rate, the more nuclei that will form and thus the greater number of crystals of smaller size.  Also, the rate of cooling will secondarily affect the crystalline morphology of polymers.  The slower the cooling, the larger the crystals.  Because of this, crystalline polymers tend to be more dense than amorphous polymers and the appearance of crystalline polymers without colorants will generally be a milky translucent white, and never clear at room temperature as opposed to amorphous polymers which can (as natural, uncolored resins) be clear at room temperature.

Some examples of crystalline polymers are: Polyethylene (PE) - including LDPE, HDPE, & UHMWPE, Polypropylene (PP), Polyoxymethylene (POM - Acetal - Celcon, Celstran, Delrin), Polyamide (Nylon 6, 6/6, etc), Polyethersulphone (PES), Polyesters (PBT, PET, PCT), Syndiotactic Polystyrene, etc.

So when you're thinking about crystalline and amorphous polymers the analogy to a pile of sticks or a plate of spaghetti works well in thinking about the differences in their physical properties and their flow behaviors.

Classification of Polymers - Thermoplastics and Thermosets

I know a few students out there who are taking classes in polymer science this term at Kettering University and I thought I would provide some study materials.   Of course I'm happy to take suggestions or answer questions from students as they arise.

On the topic of polymer classification, this is one of the first things that students should be learning about polymers.  This of course assumes that we all are of the understanding that polymers are chemically based materials comprised of long chains of carbon atoms that may also have side-chains that affect the properties of the material as a whole.  Polymers are created via chemical reaction of a monomer or a mix of reactants each with at least two active sites on the molecules.  During the reaction, the chains grow until there is little or no monomer (or reactant) available to continue the reaction.  The size of the chain determines the molecular weight of the polymer.

The first thing everyone should know about any polymer is whether it's a thermoplastic or a thermoset.  Thermoplastics, as the name suggests, are polymers that can be melted and reformed again and again.  This is like candle wax, butter, or chocolate.  Thermosets, as the name suggests, set with heat and do NOT remelt.  Think of an egg; once it's cooked, it's done.  There's no remelting an egg once cooked.  This is because the reaction involves cross-linking between polymer chains.  Heating the set polymer will cause expansion of the molecules but the cross linking will prevent the chains from slipping past one another.  Thermoplastics are polymerized from monomers with two and ONLY two active sites on the molecules.  Thermosets are formed from monomers and reactants with three or more active sites on the molecules.

SO...

When it comes to recycling, Thermoplastics have many uses after recycling where-as thermosets are good for little more than road asphalt filler.