Solution:

811105 is the highest number that can be formed moving two matchsticks.

If your answer was 511108, you're almost right. All you have to do is look at that upside down. See the first picture and then the second.

Solution:

The next three digits will be 138, 150 and 180.

If you analyze, you will find that all the numbers are increasing in order and are surrounded by two prime numbers.

For example, 4 is surrounded by 3 and 5; both are prime numbers.
6 is surrounded by 5 and 7; both are prime numbers.

Solution:

Three blind mice.

Explanation.
There are no i's in mice

Solution:

19

Explanation:
The children can purchase 19 chocolates in return.

Out of 77 wrappers, 75 will be used to buy 15 chocolates and two will be left spare.
The 15 chocolates will create 15 empty wrappers that can be exchanged to get three chocolates.
Three chocolates will return three wrappers which will help them buy another chocolate.
Now the wrapper from this chocolate and the two spare that were left earlier will get them another chocolate.
15 + 3 + 1 = 19

Solution:

There is a simple logic to solve this question.
The size of the chocolate is 2 x 8. Thus, you need to have 2 x 8 = 16 pieces.
Every time you break the chocolate, you will get one extra piece.
Thus, to get 16 pieces, you must break it (16 - 1) = 15 times.

Solution:

Both S and T are of same height because they are the same people.

Suppose that each person is marked with their respective number which also denotes their height.
Now when the longest from each row is called out, they will be 50, 100, 150 ... 500. Shortest among them will be 50 aka S.
When the shortest from each colum is called out, they will be 1, 2, 3, ....50. Longest among them will be 50 aka T.

Thus, they both are same person.

Solution:

The best way to increase the probability of winning is to place one yellow ball in the first bowl and all the other balls in the second bowl.

Now, you have a 1/2 probability of choosing the bowl with just one yellow ball. If you choose that, you win.

If you choose the other bowl, it has 49 yellow balls and 50 white balls. You still have almost 1/2 probability of picking a yellow ball out of it and winning.

Solution:

There are 24 squares in this picture.

Solution:

Nice Personality.

Explanation:
N + ice + Purse on "ality" =>Nice Personality

Solution:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.