***  Dottown Solution:  Part I  ***

We know, and all of the residents of Dottown know, that if there
is exactly one red dot, the person with the red dot will die
Night 0 (the night of Day 0) and not be there at noon on Day 1.

If JQP sees exactly one red dot, then either (a) there is only
one red dot (on JRP0, say) or (b) there are exactly two red dots.
If JQP sees that JRP0 is still alive on Day 1, JQP knows that
there must be two red dots, thus JQP must have a red dot.  JRP0
comes to the same conclusion, so JQP and JRP0 (the only two with
red dots) die on Night 1.

Remember that all of the residents with blue dots see two red
dots, so they're wondering whether there are exactly two red
dots or exactly three red dots.  Thus, all the JBPs (residents
with blue dots) don't die when the JRPs die.  The JBPs will
notice at noon one day that all the JRPs are gone, so they will
die that night.

We apply mathematical induction.  We've shown what happens when
R = 1 (exactly one red dot) and when R = 2.  Now, assume we know
what happens when R = N (for a given N), and show what happens
when R = N + 1; this is the inductive step.  

Let R = N.  Assume that all JRPs will deduce their dot color on
Day (N - 1) and die Night (N - 1), and all JBPs will deduce
their color on Day N and die Night N.  This is our `given';
we've already shown this to be true for N = 1 and N = 2.
What happens if R = N + 1 ?  For a JRP, R_v = N, but JRP doesn't
know whether R = N or R = N + 1.  When JRP sees everyone still
alive on Day N, however, JRP will realize that R = N + 1; if 
R = N held, all the red-dot people would be gone on Day N.

Thus, the answer:

*   If there are N persons with red dots in Dottown, the persons
*   with red dots will deduce their color on Day (N - 1) and die
*   Night (N - 1).  The persons with blue dots will deduce their
*   color on Day N and die Night N.


I apologize if my switching back and forth between descriptive
narrative and mathematical notation has been confusing.  I
haven't taken the time to be completely consistent (or
rigorous).


Now for an interesting addendum  :-)  :

Say that there are several residents with red dots---at least
two and perhaps many more.  Everyone in Dottown sees at least
one red dot, and the town has lived in peace with no deaths for
years.  Now, this stranger comes in and announces,  ``There is
at least one person in town with a red dot.''  Everyone knew
this already!  All could see from direct observation that this
was true.  Why does the stranger's statement make any difference
whatsoever when everyone already knew the truth of what the
stranger said?

The solution to the addendum is in  Dottown Solution:  Part II.