I am an odd number. Take away a letter and I become even. What number am I?

Prove that the below maths equation is true.

8 + 8 = 91

An inspection by the superintendent of St. Joseph School was scheduled on the next day. The class teacher Jenifer knew that he would be asking questions from her class and she would have to choose a pupil to answer. To offer a perfect impression over him, the teacher explained certain instructions to the students to maximise the chances of getting correct answer every time.

What did she say to the students?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

On a special event at the prison, 5 prisoners John, Jacob, Krist, Tang, and Dang given a chance to go to a sauna and can bring one thing with them.

Following are the things that the prisoners bring with them.
John: A soda
Jacob: Thermos
Krist: Book named "How to kill"
Tang: A Walkman
Dang: Harmonica

Since it is a Sauna, no one can see each other. After a while When the steam is switched, Tang was found dead and there was blood all around.
J Bond was called and he instantly come to know who can be the murderer. How?

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."?

Can you count the number of triangles in the given picture?