A student writes: 


  Dr. Patt,

  For Question 10, it says that the coke controller "that only takes the 
  following three inputs: nickel, dime, and quarter."  Does this mean 
  that there is only ONE nickel, ONE quarter, and ONE dime?  

  <<...you know -- I deleted his name>>

Normally, I would not forward this to you, but it points up something 
important that you should be aware of: misinterpreting a problem in such 
a way that the problem goes from very hard to very easy.

First, my response to the student:

I guess you could interpret the problem that way.  

But then the nickel would be superfluous.  In fact, the whole issue 
of the machine giving change would be moot.    Certainly, if you had 
one nickel, one dime and one quarter, and you put in the nickel and 
dime first, the machine would give you a coke and change after you also 
put in the quarter.  But would you really put in all three coins if cokes 
were 35 cents?

Also is it reasonable to assume that a coke machine would take a quarter 
and a dime, but not a quarter and two nickels?

It would certainly make the problem easier.

The intent of the problem was that the input to the machine (like all the 
coke machines that I am used to) is you put in coins one at a time, as 
many as you need to, and each coin has to be one of the three coins specified.  
For example, if you put in successively seven nickels, after the seventh 
nickel, you would get a coke and no change.

Finally, I want to thank you for asking.  It shows that you had an innate 
sense that maybe your interpretation of the problem was not correct.  One 
of the things an engineer must have to be successful is good common sense. 
That means interpreting the question correctly, unless the question is 
worded so badly that such is impossible to do.

So, if you have a concern about your interpretation of a problem, please 
ask (as you did) rather than assume a simple problem which you can easily 
solve.  If you do the latter, and I feel your interpretation changes the 
problem from challenging to trivial, the chances are: no points.

Yale Patt