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.

81 x 9 = 801. What must you do to make the this equation true?

I have branches, but no fruit, trunk or leaves. What am I?

Can you count the number of lines in the below picture?

What can you hold in your right hand, but never in your left hand?

My thunder comes before the lightning; my lightning comes before clouds; my rain dries all the land it touches. What am I?

No matter how little or how much you use me, you change me every month. What am I?

A newspaper is supposed to have 60 pages, but pages 24 and 41 are missing.
Which other pages won't be there?

What kind of storm is always in a rush?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?