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?

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

I cannot talk, but I always reply when spoken to. What am I?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Decode below rebus
D
N
A
T
S , D

I noticed one of the words in the oxford dictionary is spelled incorrectly. What about you?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

What goes up but never comes down?