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.

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

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 each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.