Solution:

In Mansion M2, we know that older child is boy, therefore there are two cases
Older Younger
Boy Girl
Boy Boy
Probability of at least one girl child: 1/2 => 50%

In Mansion M1 there are three cases
Older Younger
Boy Girl
Boy Boy
Girl Boy
Probability of at least one girl child: 2/3 => 66.67%

Solution:

The attached picture gives away the solution. If you can find another solution, do send us yours.

Solution:

On Your lap.

Solution:

This problem can be solved with algebra as well as logical reasoning. We are going to tell you how it is logically possible.

Be it any quantity that was present in the beginning and any liquid as well. We know that we have taken a spoonful from one glass and put it into another. Then, we have taken a spoonful from the other glass and put it into the first glass. So, at the end of it, the quantity of liquid in either glass remains same as it was in the beginning.

Therefore, we can conclude the fact that any amount of coke that is missing in the glass with coke will be present in the lemonade glass. Also, the same quantity of lemonade will be missing from the lemonade glass and will be present in the coke glass.

Solution:

Steps:
1) Light fire on first bar from both the ends and second bar from one end.

2) After 30 seconds(when first bar gets completely burned out) , burn the second bar from second end as well.

3) When second run completely gets burned , you know its 45 seconds.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.

Solution:

There are three roses and four bees.

Solution:

See the colored sticks in the picture. We have moved those sticks in the position given in the second image corresponding with the color.

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

The wise man told them to switch the horses and then race. In this manner, both of them will be willing to race as fast as they can to prove that the other horse (his own horse) is slow.

Solution:

It can be solved as below.