What is both possible and impossible at the same time?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

Can you find a five letter word that is left with only two letters if one is removed?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

Solve this tricky question. You are trapped in a forest. With you, you have a gun preloaded with two bullets in it. In front of you, there is a tiger, a leopard and a jaguar.

How do you survive?

O_er_t_o_

Complete the missing letters of the given word.

It's been the first day of the school when a young girl was found raped and murdered.
Police suspect four male teachers as on the killers and ask them what they were doing in the morning in time 8:00 am.
1. Wayne: I was reading the newspaper.
2. Terry: I was checking chemistry papers
3. Bridge: I had locked myself in my room as my wife left me.
4. Cole: I dropped my wife to her office.

Who is the killer?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

Who has married many women but was never married?