Find the next number in the sequence

1, 2, 6, 21, 88, __?

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?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

In the Mexico City area, there are two Houses H1 and H2. Both H1 and H2 have two children each.
In House H1, The boy plays for Mexico Youth academy and the other child plays baseball.
In House H2, The boy Plays soccer for his school in Mexico and they recently have a newborn.

Can you prove that the probability of House-H1 having a girl child is more than that of House-H2?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?

Which number should replace the question mark?

What's a single-digit number with no value?

The more it dries, the wetter it becomes. Can you tell what it is?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?