How many letters are in the alphabet?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

The Puzzle: A girl, a boy, and a dog start walking down a road.

They start at the same time, from the same point, in the same direction.

The boy walks at 5 km/h, the girl at 6 km/h.

The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn.
How far does the dog travel in 1 hour?

It is raining today at 11:59 am. What is the probability of sunny weather after 72 hours?

A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them into two equal halves.

Can you help him divide the land in a manner that both of his sons will be happy?

I know a number which is spelt in alphabetical order.
Do you?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.