Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

Why Wine Glass Stem is so long?

Wednesday, Steve and Pam go to a restaurant to eat lunch. After eating lunch, they pay the bill. But Steve and Pam do not pay the bill. So…who does?

Can you count the number of seconds in a year?

Clue: You need to bother about calculation.

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

Jack looks at the 4 cards i gave him, and says out loud which card Joseph is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Jack needs to know is the order of the cards and what is on their face, nothing more.