If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

What type of tree can I carry in my hand?

There is a certain crime, that if it is attempted, is punishable, but if it is committed, is not punishable. What is the crime?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

If an earthquake is 1 point higher on the Richter Scale than another earthquake which is actually 10 times stronger, how much stronger would an earthquake be if it was just half a point higher on the Richter scale?

Remove two matchsticks to make the below equation correct.

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

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?