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.

Can you complete the sequence puzzle?

AR TA GE CA LE VI LI _

How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

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?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see? What is it?

Can you fill the blank with the correct number?

6 30 870 756030 _____

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.