Which is the rope you never skip with?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

Can you start the fire using two pieces of wood?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

Sherlock breaks into a crime scene. The victim is the owner who is slumped dead on a chair and have a bullet hole in his head. A gun lies on the floor and a cassette recorder is found on the table. On pressing the play button, Sherlock hears the message 'I have committed sins in my life and now I offer my soul to the great Lord' and followed a gunshot Sherlock smiles and informed the police that's its a murder.

Why did he think so?

Can you replace the question mark with the correct letter?

6 + 6 + 6 = N
7 + 7 + 7 = E
8 + 8 + 8 = R
0 + 0 + 0 = ?