Solution:

Step 1) Pour 1 liter of Water from gallon A to gallon C. Now 4 liter of Water is left in the gallon A and gallon C is full.

Step 2) Pour Water from gallon C to gallon B. Now as soon as gallon B is full , you know there is one liter of Water is in gallon C.

Solution:

It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.

Solution:

1/3

This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.

The following are possible combinations of two children that form a sample space in any earthly family:

Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl

Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.
This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3

Solution:

5

23-2=21
21+3=24
24-5=19
19+7=26
26-11=15
15+13=28
28-17=11
11+19=30
30-23=7
7+29=36
36-31=5


(2,3,5,7,11,13,17,19,23,29,31,37,41,43... are Prime Numbers)

Solution:

24 13 11 5
----------
24 0 0 0
11 13 0 0
6 13 0 5
6 2 11 5
8 0 11 5
8 5 11 0
8 13 3 0
8 8 3 5
8 8 8 0