Miscellaneous quizzes.

I've come up with random ideas now and then and I thought it'd be fun to have a quiz gallery here on SP.net. So guys, post away, compose, resolve, criticize our quizzes, whatever. Quizzes of any subject should be fine, only one condition is required: be sensical please.

To start off, I have two for you here.

1.) Fun with numbers: Find the next number of the sequence:
1, 5, 9, 17, 27, 33, 51, 65, ...
Hint1: Do geese see God?
Hint2: You might want to adopt a different approach to the numbers. A more... Fiel-ish approach.

2.) Fun with image: What is this?

3.a) An old king is about to die and he has no offspring to inherit the crown. So he summons the three wisest men from his kingdom and puts them to a test. He tells them that he is about to put them in a room and have his aide put a hat on each of them. Each hat may or may not have a dot on it, but at least one hat will have a dot. They may not touch the hats, nor communicate in any way. The first one that correctly identifies whether his hat has a dot will become the next king. If he is wrong, or if he breaks the rules, he will be killed. Then he sends all three wise men into the room.

The king then tells his aide to put dotted hats on all three.

A few minutes later one of the wise men returns and announces proudly that he has a dot. How did he know?

3.b) Logical reasoning: Stolen from someone below
Three criminals are given a chance for survival if they prove their brains to be of use. They are put in a room, arms and legs locked, they are not allowed to communicate with each other in any way, and they do behave, seeing as their asses were glued to the electrocution chairs. They are put to sit on a straight line, facing the same direction (so that the one(s) behind can see the one(s) in front of him only.)
The catch is, at least one of them has a weightless, feel-less hat on his head and if he can announce that he's wearing it, they're all free, otherwise, they're all dead. After a long pause of silence, one of them shouted out and they all lived together happily ever after. How?

4.) There are 100 coins scattered in a dark room. 90 have heads facing up and 10 have tails up. You cannot distinguish (by feel, etc.) which coins are which. How do you sort the coins into two piles that contain the same number of tails?

Hints will be provided in due time.

Second is definitely a laser beam.

looks like a bird to me

Actually I could give hints, but with google it'll be too obvious and spoil the fun. =/

Second one is obviously Two turntables and a microphone.

1. The answer is obviously "..."

Not "..."

Hint: Do geese see God?

79

Nope. Anyone? Maybe someone with a few more quizzes?

1. 42

1. 83
2. a picture

Answer to the first question is 56.

I'm interested in your reasonings behind those numbers. Or are they just Funhouse-styled randomized?

"Do geese see God" is a palindrome.

Thought you wanted to repeat the list of numbers like in a palindrome.

1 + 65 = 66
5 + 51 = 56
9 + 33 = 42
17+27 = 44
Continuing that, 40...? Dx

2nd one is a kitten, as seen from the 4th dimension.

"Do geese see God" is a palindrome.

Thought you wanted to repeat the list of numbers like in a palindrome.

Yes it is a palindrome, but you still need another key to open the chest.

last guess: 75

last guess: 75

One down. Bacon next. I CHALLENGE YOU!

Requesting Black elephant