Why 1729 is a magic number? Answer Logically.

What is both possible and impossible at the same time?

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?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

I was speeding and ran through a stop sign, yet two traffic officers who were there do nothing about it.

why?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it?

Some friends went on a vacation to a resort. It was raining heavily and it kept raining for thirteen days.

When it rained in the morning, the afternoon was beautiful and when it rained in the afternoon, the day was blessed with a clear morning.

Overall, the friends experienced eleven nice mornings and twelve nice afternoons. Can you find out the number of days they spent on vacation?