I shave every day, but my beard stays the same. What am I?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

There's a day, that comes around once a year.
To celebrate the man, you hold dear.
He gave you life, love and will pick you up if you fall.
When it comes to guys like him, He's the best of all.
Who is he?

Sachin bought a car with a strange 5 digit numbered plate.The water image of the number is 78633 more than my car number. All the digits of car number are distinct.

What is the original number on number plate?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?

Suppose you are sitting in an interview and the interviewee asks you an aptitude question.

You have three buckets with a capacity of 4 litres, 8 litres and 10 litres and you have a large tank of water. Now you have to measure 3 litres of water precisely using those buckets. How will you do it?

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?