A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

Count the number of balls in picture below: