Brain Teasers

1. Girl or Boy?
Teanchi and Beanchi are a married couple with two children.  One of them is a girl. What is the probability that the other one is also a girl?
Ans: We can assume that the probability of a couple getting a girl or a boy is half. This is in general true if we do not have any more information about the gender of the children. Now, we already know that one of the children is a girl.
We have to apply what is called conditional probability: given that one child is a girl, what is the probability that the other one is also a girl. We have to make use of this information as follows.
There are four possible combinations:
Girl - Girl
Girl - Boy
Boy - Girl
Boy - Boy
Since we know one of the children is a girl, we will drop the Boy-Boy possibility from the sample space.  This leaves only three possibilities, of which only one possibility is both girls. Hence the probability is one out of three or 1/3.
So, without knowing any information the probability of the parents having two daughters is 1/4. But if you already know that one child is a girl, the probalility that the other one is also a girl is 1/3.
2. Fly Logic Puzzle
Two trains, 200 km apart, are moving toward each other at the speed of 50 km/hour each. Just as they begin their simultaneous journey, a fly takes off from one train flying straight toward the other at the speed of 75 km/hour. Having reached the other train, the fly bounces off it and flies back to the first train. The fly repeats the trip until the trains collide and the bug is squashed.  What distance has the fly traveled until its death?
Ans: There is an easy way of solving this puzzle. Each train is going at the same speed of 50 km/hour. They are traveling in opposite directions towards each other. So the distance between the trains is decreasing at a rate equal to the sum of the speed of each train, or 100 km/hour. They are initially 200 km apart. So it will take 2 hours to close the gap.
This means that the trains will meet/collide in 2 hrs. So the fly is going to be squashed in two hours from the starting time. Instead of painfully following the journey of the fly up and down between the trains, it is simpler to ask the question: how far can the fly travel in these two hours, if it is always travelling at 75 km/hr. The answer is of course 150 km. (We assume that the fly doesn't slow down at the turning points).
2. Sequence Puzzle
Below is a number puzzle. It should be read left to right, top to bottom. The first five rows are filled.

       1
      1 1
      2 1
    1 2 1 1
  1 1 1 2 2 1
  ? ? ? ? ? ?
? ? ? ? ? ? ? ?

Can you fill the next two rows of numbers? How did you get this answer?
Ans: This is a trick question. To answer it you have to read the lines out loud. What you see on each line becomes the next line!
For example, on the first line you see one 1. So the second line is 1 1 (which you will read as "one 1". But what you now see on the second line are two ones! So obviously on the third line you will write "2 1". You will now see that the third line contains one 2 and one 1. So you will write down "1 2 1 1" and that becomes the fourth line and so on.
To summarise:
Line 1 has one 1.
Line 2 is "One one" (1 1)
Line 3 is "Two ones" (2 1)
Line 4 then becomes "One two, and one one" (1 2 1 1)
Line 5 therefore is "One one, one two and two ones" (1 1 1 2 2 1)
Line 4 is "Three ones, two twos and one one" (3 1 2 2 1 1)
Line 5 is "One three, one one, two twos and two ones" (1 3 1 1 2 2 1 1)
The answer to the unknown lines therefore becomes 
  3 1 2 2 1 1
1 3 1 1 2 2 2 1
-From brainden.com