Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.

Solution:

There is no smoke with an electric train.

Solution:

33 seconds

The train takes 30 seconds to travel 1 mile, plus 3 seconds for the complete train to pass any point, making a total of 33 seconds.

Solution:

The chances that the pair you take out is a white pair is zero.

Just analyze the statement carefully. If there are two colored socks in a drawer, there can be three chances if you take out a pair. It can be either black socks or white socks or a mixed of two. But as per the statement the chances of taking out a black pair of socks is 1/2. Therefore, only two chances exist. We do know that there is a mix of white and black socks in the drawer and thus the second chance has to be a mixture of them both. This is the reason why we can deduce that there are three black socks in the drawer and just one white sock. Thus the probability of taking out two white socks will be zero.