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.

There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even-numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth? and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progress similarly.

After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off?

What goes up but never comes down?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

Use only one mathematical symbol and all numbers (0-9) to get a sum of 99

Solve the following series:
AZ, GT, MN, __, YB

Usually, a boxing match consists of twelve rounds. In a particular friendly match between two heavyweights, the match was finished in the ninth round itself as one of the boxers knocked out the other one.

But, in that fight, no man threw even a single punch.

How can this be possible?

Which tank will fill first?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

I look at you, you look at me, I raise my right, you raise your left. What am I?