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?

With the help clues provided in the image, can you find the 5 digit key?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

what does this picture(rebus) riddle means ?

If we tie a Sheep to one peg, a circled grass is been eaten by the Sheep. If we tie the Sheep to two pegs with a circle on its neck, then an eclipse is eaten out of the grass by the Sheep. If we want an eclipse then we put two pegs and then put a rope in between them and the other end of the rope is tied up on the Sheep's neck.

How should we tie the peg and the Sheep so that a square is eaten out from the garden grass? We only have one Sheep rope and the peg and the rings.

Out of four images which one is the odd one out?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.