Prove that the below maths equation is true.

8 + 8 = 91

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

A bridge is about to collapse. There are four people P, Q, R and S on one of the sides. Before the bridge collapses, they want to cross it. Now since the bridge is too weak, it can only stand the weight of two people at a time. Also, it is night time and nothing is visible. They have just one torch with them.

Now P takes one minute to cross the bridge, Q takes two minutes to cross, R takes five minutes to cross and S takes ten minutes to cross.

The bridge will collapse in seventeen minutes. How will they be able to cross the bridge before it collapses?

Daniel walks into a movie theatre. While in the movie, he suddenly smiles delightfully. About a couple of minutes later, he seems shocked. He walks out of the theatre, goes to a bridge and jumps over the edge killing himself.

Why did he do it?

Note: Think Lateral

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

What does the below rebus riddle means?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?

Which digit occurred maximum times between the number 1 and 1000?