Replace the question mark with the number below given a simple math problem.

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

Steffi's daughter Jazelle needs to be picked up from school every day.
Steffi asks one of her colleagues to pick up Jazelle from the school. Steffi devised a password system to confirm that Jazelle goes with the correct colleague only.

The password on Monday was SJM16.
The password on Wednesday was TAW39.

What will the password be for Friday?

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

In a particular village, only two barbershops exist.

The first shop has a handsome barber with a neat haircut who is handsomely dressed in clean clothes and is extremely humble with his body language. The place is clean and looks hygienic.

In the second shop, you can find a barber with shabby clothing. His hairs are weirdly cut and his clothes still have the stains from last night's dinner. The place is not clean as well and reeks a bit.

You visit the village for the first time and decide to get your haircut. Which barbershop will you like to go for that and why?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?