Can you spot the hidden girl in the picture below?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

Why is 6 afraid of 7?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

Replace the question mark with the number below given a simple math problem.

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
=========

I am lying and I always lie. Tell me whether I am lying or telling the truth.

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?