Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

John was born on March 5, 1970, in Delhi, India. Jacob was born 25 days before John. The year when they took birth, Republic Day fell on Monday.

Can you find out on what day was Jacob born?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

What four weights can be used to balance from 1 to 30 pounds?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

It belongs to you, but other people use it more than you do. What is it?

Move four matchsticks to the below square to form three squares?

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.