I was just reading the first post and got different answers for these two questions. Feel free to comment 
I got 1hour, 5 minutes, 5.0847 seconds...
12 1 2
+----------+----------+
min hour
hand hand
can be interpreted as
0 5 10
+----------+----------+
min hour
hand hand
at 1pm the minute hand is at 12 position, the hour hand is at 1 position.
The minute hand travels at 1 per minute
The hour hand travels at 1/60 per minute
at intersection, 5 + t/60 = t
Hence t=300/59= 5 min 5.0847... sec
There are 2 possible outcomes to this set up. But I found some are more likely than others:
Say the circle is divided into A and B and the points P1, P2, P3. Area A = Area B hence prob(each point in each semi circle) = 0.5
Hence if you draw a probability tree, you'd find the probability is 1/4.
Let a= \(\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\ldots}}}} \)
ln(a)
= 1/2 x ln2 + 1/4 x ln 2 + 1/8 x ln2 + ...
=ln2 (1/(1-0.5))
=> a=4
