Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

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.

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?

Steffi's daughter Jazelle needs to be picked up from school every day.
Steffi asks one of her colleagues to pick up Jazelle from the school. Steffi devised a password system to confirm that Jazelle goes with the correct colleague only.

The password on Monday was SJM16.
The password on Wednesday was TAW39.

What will the password be for Friday?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

Why do we preferably have round manhole covers and not square ones?

Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()