Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

If,

Akriti = 631
Levis = 521
Sroti = 521
Aneel = 533
Then,
Sunil =?

Okay before we begin with the puzzle, do keep in mind that you have to answer it quickly.

You are participating in a car race. Seeking the perfect moment, you overtake the second person in the race. What positions are you in now?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?