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What is a trillion between friends?

1. In todays money ($US) just the difference of a tera-dollars and a trillion dollars would
(a) buy you a house in Los Altos Hills, California
(b) buy all of Los Altos Hills.
(c) have you rival Bill Gates in net worth.
(d) probably score you a small country
ans.

2. How much is 1 tera of  H₂0 molecules? It is
   
(a) roughly the volume of a can of diet coke.
(b) 30 femto-liters.
(c) a small tub full.
(d) 3.1415 ml.
ans.

3. If you, as the writer Issac Asimov once suggested in one of his fictional works, were to store information by notching individual atoms off of molecules, how long would a 1 Tera byte chain be?  ( For the sake of this exercise assume that the simplest way to store information is the bi polymeric chain of A and B components where A and B are monomer representing 0's and 1's.  )
(a)  2.6 km
(b)  2.6 nanometer
(c)  2.6 meters
(d)  2,600 km
(d)  2.6 mm
ans.

4. As the numbers grow larger due to the root difference or the relative error between the International System of Units (SI) and the binary prefixes go out of wack. With 1 killo and 1000, the deviation represents a 2.4% the value, 1 mega  to 1,000,000 deviates 5% and 1T to 1 trillion of 10%.  When does an  intolerably large error of say 50+% occur?
(a) so far out in the future that there is no need to worry
(b) by the year 2013
(c) by the year 2015
(d) by the year 2042
ans.


Theory and Probability

5. Theoretically speaking, what would a potential application or purpose of a virtual constructor be?
   (a) It is useful to construct a subclass object whom you only know some external way of specifying the subclass, such as a string input.
   (b) It could theoretically be the formal implementation of virtual base class definition of clone and create.
   (c) It permits the full release of resources of an object through calling the proper destruction chain even when you are operating on an object through a pointer or reference to its base class.
   (d) All of the above.
   ans.
6. Given that a valued prize is hidden behind one of three doors.  You must select correct door to win the prize, however once you make your initial guess a knowing game host reveals one of the empty doors.  At this point you are given the opportunity to change your initial guess in favor of the only remaining door.  What should you do, and what is the probability of obtaining the prize given this choice?
   
   (a) You should stay put your probability of winning is as good as it will be if you change at 33%.
   (b) You should definitely make the switch as your probability once switched is now 50%.
   (c)  It does not matter if you make a switch or not as your probability either way is 50%.
   (d) None of the above.
   ans.
   

1. The difference is a mere $500M shy of the $100B mark.  If you picked (a) my cousins are selling.  If you picked (b) they could convince their neighbors to sell too.  If you selected (c) Bill Gates you are correct assuming the MSFT stock is still relatively flat ( October 2005, MSFT last double of value brings you back to 1997 )You now top the Forbes top ten list in net worth.  Regarding  (d) , assuming a multiple of 10-20 times the GDP would do, $100B should definitely score 20 island or small African nations and even some mid size countries like Madagascar, Georgia, etc.(ref. wiki ) .
   questions.
   
2. 1 tera H₂O molecules is (c)
   
   1099511627776 *  18 grams/6.0E23 AvNum *  .001 L/gram = 3E-14 L = 30 fL
   

   questions.
   
3. Given simplest monomers you can use are polyethylene(–(CH₂-CH₂)_n–) and polypropylene (–[CH₂-CH(CH₃)]_n–), where the methyl group (CH3) is the "atom" functional group storing the "1" .  A chain of 01010011 would look like ABABAABB, or The chain unit has the unit length of approximately 3 angstroms (3E-10 meters) so the total length of a tera byte chain would be
   HCH₂-CH₂–CH₂-CH(CH₃)–CH₂-CH₂–CH₂-CH(CH₃)-CH₂-CH₂–CH₂-CH₂–CH₂-CH(CH₃)-CH₂-CH(CH₃)
   1099511627776 bytes * 8 bits/byte * 3e-10 meter/bit= 2.6 km.  Answer (a).
   
   Mind you that it would be a very thin string taking, when bunched up, not much more space than the water in question 2 -  just a few femto-liters.

Note: Chemical structures grow combinatorially, so the simplest bi polymer, the polyethylene polypropylene bi polymer is not likely the densest possible format.  If one had the technology to rapidly build and read a specified chain of two different monomers, one should presume that they would be able to select a myriad of just slightly larger molecules .  With a slight increase in atoms the larger molecules could permute in to a large base X number system.

questions.

4. I believe (a).  You do not need to worry, by the time you get as far out as the 21st suffix all the good alphabet symbols are pretty much taken up anyways.  Perhaps another notation similar to scientific notation (e.g. speed of light 2.99e8) will replace letter suffixes.  As for the answer (b) in the year 2013 assuming if Moor's Law holds we will be still working our way through P (peta) or Quadrillion which has an error of a perhaps tolerable 13%.   The rest of the options 2015 and 2042 are there to just throw you off.  Perhaps you just choose 2015 because it was closely grouped to 2013 and in the middle?
   questions.
   
5. The correct answer is (b), although my first inclination was that it was strictly Dirk Gentley stuff, I saw a good argument on the web (at parashift) for its potential practical use.  A dynamic abstract class definition first must be added to  C++ so you can somehow still specify the class& of interest.
   

   Dirk Gentley is a fictional detective, a creation of  Douglas Adams and the kind of gumshoe who would follow random automobiles under the premise that while following random people, "he would rarely go to where he was heading for, but the destination was almost always very interesting."

   questions.
   
6. Unambiguously (d) "None of the above." is the correct answer.  If your choice was (a) then why would you not want to sweeten your odds a bit given that you now have some inside information.  Your probability of 1/3 here is absolutely true however and thus the revealing the perhaps unintuitive truth of this problem.  The probability of all the states any system sums to 1.  This if 1/3 of the probability goes to your initial guess the other 2/3 are evenly distributed to the remaining two doors ... that is until someone reveals one of the cards as not  the prize card.  Following this, the probability distribution must readjust to the remaining unselected face down card.  In summary you should select the not yet selected, not yet revealed card as it holds a 2/3 chance of being the prize card.  If you don't believe me and particularly if you guessed (b) then you are in good company with the famous mathematician Paul Erdos whose initial trouble with this problem is described in The Man Who Loved Only Numbers.  You may look up the problem as The Cadillac Problem, or else download my CadillacProgram and run a simulation of it for yourself.  
   
   
$ time ./CadillacProblem.exe 1073741824
of 1073741824 trials

Strategy "keep first choice" wins :  357915152   (33.333446)
Strategy "Switch door"       wins :  715826672   (66.666554)
                                  -----------   ----------
                            total : 1073741824   (100.000000)

real    11m46.656s
user    0m0.015s
sys     0m0.000s

   
   questions.

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