HINT FOR PUZZLE 2

STEP:1
Well.Taking the first step along with the drunkard is easy.Is'nt it?
After the first step,we expect him to be at a distance R from the lamp post-more specifically he can be at any point on the circumference of a circle with the lamp post as the centre and radius 'R'

STEP:2
Now one can pick any one point (say O')on the circumference of the above mentioned circle.Supposing he had been at this point after the first step, where all could he have gone with the second step?
Once this aspect is clear,one needs to calculate the following.
For this chosen point O',effectively what would be the expected distance from the lamp post after the second step? You can now extend this logic for all the other points of the first circle.
STEP:3 Once we are clear with the first two steps the rest will follow logically.

ANSWER

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