How many words can a pen with half refill write?

What is the next number in the series?

15 29 56 108 208 ?

Give it food and it will live; give it water and it will die.

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

What you cannot hold but it is yours?

There are three Athletes (John, Tarun and Harish) and their individual Coaches (Jacob, Meenaxi and Priyanka) standing on the shore.
No Coach trusts their Athlete to be near any other Coach unless they are also with them.
There is a boat that can hold a maximum of two persons.
How can the six people get across the river?

What brings you down but never up?

what does this below rebus represent identXQQQQQME