This one provides an opportunity for me to reinforce the notions of 
state, etc., so I am forwarding his question and my answer.  If you 
feel you are solid on the coke machine, feel free to simply delete 
it.  I am concerned that I am in overkill mode.

Anyhow, a student writes:

	Dear Sir,

	I have a problem in Q-10.   The number of circles of
	states that I make exceeds the hinted number of seven.

Read the hint again.

       I created circles of 35, 30, 25, 20, 15, 10, 5,
       bingo, and then bingo+5 change, 15 change, and 20
       change.   Now my questions:

       1. Is it fine if the number of states I have exceeds
       the number hinted?

Sure.  But you should try to understand what the hint is driving at.  
I don't make hints idly.  As it is, I don't think you are reading 
the hint correctly.

       2. Can we consider a situation also, where a person
       drops six nickels one at a time, and then a quarter?  
       This is just an example, but its answer shall clarify
       my doubt.

Absolutely.  A person can drop 6 nickels + a quarter.

	     3. Do we have to create separate states for different
	     amounts of change to be given?   You may not answer to
	     this if not considered proper.

Yes, they produce different outputs: coke + 5 cents change is 
different output from coke + 10 cents change.

     4. Do we have to create different states for different
     values of amount left to be paid, and then have three
     possible values of moving to a next state (nickel,
     dime and quarter).   You may not answer this also if
     not considered proper.

Absolutely.  If we did not have a state for different amounts left 
to be paid, how would we know what more has to be inserted in order 
to get that coke.

	     I look forward to your response.
	     I am sorry for asking this question so late.

Not at all.  I am sorry for answering it even later.  Of course, at 
this point, the answer is all about understanding the material, not 
squeezing 1/10 of a point on the problem set.

    Thank you very much

My pleasure,
Yale Patt

     With kind regards,

     <<...you know.>>