Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

A pack of cards has 40 cards. You are blindfolded. Out of 40, 25 cards are facing down while 15 are facing up. You have been asked to divide this pack of cards into two decks - so that each deck contains an equal number of face-up cards. Remember, you are blindfolded.

How will you do it?

A quarter is one-fourth of a dollar but Mr. John has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter with a digit to make the above solution correct?

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

During an experiment, a guy throws a bouncy ball from a 100 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up halfway.

How many bounces do you think the ball will make before it comes to a stop ?

Can you place three balls such that the equation shown in the picture holds true?