2, 3, 5, 9, 17, _ What is the next number in the sequence?

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

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?

Can you solve the rebus below?

12345 a famous South Indian actor
567 is a path in jumbled form
8 & 10 are same letters
9 is one among the first six alphabets.
WHO AM I?

Given below is simple addition with a defined pattern pattern:
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9

Can you analyze the pattern and find out the answer for:

4 + 9 = ?

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

If in a code language, DISTANCE is written as IDTUBECN and DOCUMENT is written as ODDVNTNE, the how will THURSDAY be coded as in the same language?

What is the end of everything?

The answer I give is yes, but what I mean is no. What was the question?