19.  The logic seemed to be
Odd numbers + 5
Even numbers + 6
=> 11 for 16p
(But there are other possibilities) 
20.  Identify the containers as [3] and [5]
One way of doing it is to 
Fill [3] and pour that into [5]
Fill [3] and pour as much as possible into [5]
This will leave 1 litre in [3]
Empty [5]
Pour the 1 litre from [3] into [5]
Fill [3] and pour that into [5].
There will then be 4 litres in [5].
There are other ways.

21.  It has 14 faces.
Euler's Law for solids states that number of
Faces + Vertices  Edges = 2
In this case there are 9 vertices so,
F + 9  E = 2
If there are f faces then,
there must be 3f /2 edges.
(Which means there must be an even number of faces)
So f + 9  3f /2 = 2
Solving this gives f = 14
