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

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

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

John has played 50 ODI's and his average is 50. How many runs should he score in his 51st ODI, so that his average score jumps to 51?

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

Find the next number in the series below

21 32 54 87 131 ?

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

James Bond is caught up in a mysterious scenario where the evil villain has him blindfolded. He somehow breaks through the handcuffs but is unable to get the blindfold off. Upon searching, he comes across a bow and 3 arrows. He can hear the villain speak, and thus tries to take a shot at him. He launches the first arrow, it misses the villain. He then launches the second arrow and it misses by a greater margin.

What is the probability that this third shot our James bond takes will be worse than the second shot?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?