I am a prime number.
The double of myself is equal to the square of me.

which number am I?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

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?

Can you write down eight eights so that they add up to one thousand?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Can you find out the remainder when 3^300 is divided by 5?

John drives to his office at 20km/hr. After reaching the office, he realizes that today is a holiday. He went back at an average speed of 30km/hr. Discounting the time spent in the stoppage what was the average speed of his journey?

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

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