How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

Speaking of rivers, a man calls his dog from the opposite side of the river. The dog crosses the river without getting wet, and without using a bridge or boat. How?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

What does man love more than life, hate more than death or mortal strife; That which contented men desire; the poor have, the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?