Can you find out which number multiplied by itself will give the output as 12345678987654321?

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

0 0 0 = 6
1 1 1 = 6
2 2 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

You can use any mathematical symbols in the space provided to make all above algebraic expressions true.

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?

Find the value of "?" in the ball picture Riddle below:

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

There is a straight highway. Four different villages lie on that highway. The distance between them is different. The third village is 60km away from the first village; the fourth is 40 km away from the second; the third is 10 km near to the fourth that it is to the second.

Can you calculate the distance between the fourth and the first village ?