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Planning graph blog questions..

If you *really really* understood the structure of the planning graph, you should be
able to answer these questions (add your answers to the blog)

1. If you grew the planning graph (without mutexes) to level-off and
   found that a particular literal p never entered the proposition
   list at any level. WHat is the length of the plan needed to achieve
   p from the init state? 

2. In the example above, suppose an action A never entered any action
   layer. Can you lose any plans by refusing to consider A as an
   option in the regression search (i.e., you never branch on A)? What
   about partial order planning?

3. In level 5 of the planning graph propositions p1 and p2 are not
   mutex. Is it possible for the propositions to be mutex at level 3? 
   How about level 9?

4. Suppose a planning graph with mutexes has been grown to level off
   (i.e., until two consecutive proposition levels have the same
   propositions and binary mutexes).

4.1. If propositions p, q, r appear first in level 17 with no pair of
them marked mutex. Are we guaranteed to have a plan of length 17 for
achieving p,q,r? If not, how long could the plan for p,q,r be?

4.2. If propositions p,q appear first in level 12 without mutex. Are
we guaranteed to have a plan of length 12 for them? If not, how long
can the plan be?
4.3. If proposition p appears first in level 7. Are we guaranteed to
have a plan of length 7 for achieving p? If not how long can the plan