why number 8549176320 is one of a kind?

Find The Missing Number In the Sequence.
6 25 64 ? 32 1

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

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?

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?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

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?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?