It is always ahead of me yet I can never see it. What is it?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

I have an apple tree , number of apple in this tree get doubles every week.

On 30th week , the tree gets completely filled with apples :-)



Can you tell me , on what week does my tree is half covered with apples ?

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

How many letters are in the alphabet?

Two fathers and two sons decided to go to a shop and buy some sweets upon reaching. Each of them bought 1 kg of sweet. All of them returned home after some time and found out that they had 3kg of sweets with them.

They did not eat the sweets in the way, nor threw or lose anything. Then, how can this be possible?

Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

There was a kingdom in which the king had no heir to take over his thrown. Even the queen was dead and he himself was on the verge of dying. He thought about it and then summoned all of the teenagers. He gave one seed each to all of them and asked them to grow the plant. He announced that the one with the most beautiful plant will become the king/queen of the empire after the death of the king.

After a month, all of them were called. The king looked at all of the plants but announced the girl with an empty pot as the queen of the empire. Why?