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

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

A horse was tied to a rope 5 meters long and the horses food was 15 meters away from the horse. How did the horse reach the food?

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

John was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.

A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches.

Can you help him in cracking the password?