Using Only Five 5's and any mathematical operator make sum as 37

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

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?

What is next number in the pattern below:

131 517 192 123 ?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

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

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

Our product and our sum always give the same answer. Who are we?