Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

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.

John Went to the nearby store in a Mall to buy something for her home. Below is the conversation between the two:

John: How much for the one?
Shopkeeper: It is $2
John: How much for the Eleven?
Shopkeeper: It is $4
John: How much for the Hundred?
Shopkeeper: It is $6.

What is John buying?

Complete the series by replacing "?" with the correct number.

ST ND RD TH '?'

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

PS: You may start the number from 0.

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

You can hear me, but you can't touch or see me.

What am I?

John replied, when asked how old he was. In 2 years he will be twice as old as he was five years ago.' How old is he ?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?