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.

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

I am not a bull but I have horns.
I am not an ass but I have a pack saddle.
Wherever I go, I leave silver behind me.

Who am I?

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!

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

At the local model boat club, four friends were talking about their boats.

There were a total of eight boats, two in each colour, red, green, blue and yellow. Each friend owned two boats. No friend had two boats of the same colour.

Alan didn't have a yellow boat. Brian didn't have a red boat but did have a green one. One of the friends had a yellow boat and a blue boat and another friend had a green boat and a blue boat. Charles had a yellow boat. Darren had a blue boat, but didn't have a green one.

Can you work out which friend had which coloured boats?

This is a classy optical illusion puzzle. What more you can find except bricks in the image below?

I shave every day, but my beard stays the same. What am I?

Find the smallest sentence with all the English alphabet.