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?

When we see 2 but call 10?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

What can go through glass without breaking it?

I taste better than I can smell. Who am I?

Seven Robbers robbed a bank and hide the coins in a lonely place.
They decide to divide the money equally the next morning. Two greedy robbers decided to cheat the others and reach the place at night. They equally divided the coins between them, one coin left. So they called another robber and then they decided to divide equally among the three. Sadly again one coin left. The same thing happened to the 4th 5th and the 6th robber.
However, when the 7th robber reached in the morning, they can divide the coins equally.

How many coins were there in total?

Two guards were guarding the camp.Guard-1 was looking towards the south to make sure no threat is coming from the road.Guard-2 was looking at the north to make sure no threat is coming from the top. Suddenly Guard-1 ask the Guard-2 why he is smiling?How Guard-1 knows that Guard-2 is smiling?