Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?

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?

Find the missing letter in the last circle logically in the given below picture.

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

Andrew’s doctor gives him three pills and tells him to take one every half hour. How much time will have passed by the time Andrew’s taken all three pills?