Can you find out the missing number in the grid?

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

Fate has decided that you will only be pleased to meet me when you need me

Maybe that is why, when I am working, I start working

However annoying I may be to the regulars, the little ones are always inspired

I will always be waiting if you try to reach me

How many of you can guess my name, let me see

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...