How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

There is a river to cross using a river raft and there are eight people (father, mother, policeman, thief, 2 daughters and 2 sons). No one knows to operate the raft except the adults and also excluding the thief. Only two people can go in the raft at a time. The raft should keep coming back and forth in order to pick and drop the people.
Rules to be followed:
Father: the father cannot stay in the raft or outside the raft without the presence of the mother.
Mother: the mother cannot stay in the raft or outside the rat without the presence of the father.
Thief: the thief is not allowed to stay with any of the family members unless there is a policeman.
Policeman: the policeman can travel with anyone.
2 sons and 2 daughters: they are not allowed to travel in the raft without the presence of an adult. They cannot either travel in the presence of only thieves without the policeman. The sons cannot be with their mothers without their father's supervision. The daughters are not allowed to be there with their fathers without the supervision of their mothers. But the daughters and the sons can be left unsupervised (as long as the other rules are applied).
What is the sequence that the people should follow in order to cross the river through the raft keeping in mind all the rules?
The rules are applicable not only in the raft but also outside the raft.

1 + 9 + 8 = ?
considering, 28 + 8 + 92 = 10

A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Identify the movie name through below Rebus containing Pi Mouse and coconut tree..

Find The Next Number in the series:

12 13 15 17 111 113 117 119 123 ?

Only one colour, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?