What four weights can be used to balance from 1 to 30 pounds?

What does below Rebus mean ?

esgg sgeg gegs gsge

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?

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?

Take one out and scratch my head, I am now black but once was red. What am I?

What question can you never answer yes to?

Can you replace the question mark with the correct number?

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

What is more useful when it is broken?