Replace the question mark with the number below given a simple math problem.

Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

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?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

It's a test that will check your IQ.

Suppose you have one 11 minute hourglass and one 13 minute hourglass.

Can you measure exactly fifteen minutes using them ?

There is a box full of marbles,
all but two are blue,
all but two are green,
and all but two are red.

How many marbles are in the box?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

I have Rs.50 and I spend it in the way as below.