Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles, and 2 empty bowls. He then says, 'Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die.'

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

What can you catch but never throw?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?

In the given picture, you can find two letters missing. When two particular letters are placed in the missing spots, you get an eight-letter word while reading in the anti-clockwise direction. Can you find out the missing letters and the missing word eventually?

No one wants to have it, but if one got it, he does not want to lose it. What is It?

Can you start the fire using two pieces of wood?

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?