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?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?

What is the next number in the series?

15 29 56 108 208 ?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?

From a pack of 52 cards, I placed 4 cards on the table.

I will give you 4 clues about the cards:

Clue 1: Card on left cannot be greater than the card on the right.
Clue 2: Difference between the 1st card and 3rd card is 8.
Clue 3: There is no card of an ace.
Clue 4: There are no face cards (queen, king, jacks).
Clue 5: Difference between the 2nd card and 4th card is 7.

Identify four cards?

Can you write down eight eights so that they add up to one thousand?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

How can one talk without saying a single word?

You have a square. What you have to do is cut and reassemble the square such that you create a Red Cross sign that has the same volume as that of the square.