If only one monk would be infected on day 1, he would immediatedly leave. He would see 19 people that have no signs of a disease, making him the only one infected, since the fact that there is a disease is given.

If two would be infected, everybody would see that 2 people have signs of an infection, except for two, seeing only one. Now, because everybody is unsure of their own infection, they will have to wait for one day more than the number of infected they see, to clarify their own status.

So the one seeing only one infected would know by day 2, that he is infected himself, since if the other infected would have left on day one already if he would have seen no other people with infections.

Edited 6/18/2014 11:52:50

We posted at the same time :/

25. (classic)
Some guy just died and find himself at Hell and Heaven's doors. There is two doors, one for heaven and one for hell. Two giants, brothers, are guarding the doors (one giant for each door).The dead guy doesn't know wich leads to heaven and wich leads to hell, only god and the giant brothers knows that. God then tell the dead guy that one of the guard always tell the truth, and the other guard always lies (without telling him whom is whom ofc), and that he can ask only one question to one of the guards and then has to chose wich door he wants to open.
What question can he asks, so that he is assured to go to heaven?

I ask giant no1 :" Would your brother say that behind door A is heaven?"
or
I ask giant no2 :" Would your brother say that behind door A is heaven?"
or
I ask giant no1 :" Would your brother say that behind door A is hell?"
or
I ask giant no2 :" Would your brother say that behind door A is hell?"
or
I ask giant no1 :" Would your brother say that behind door B is heaven?"
or
I ask giant no2 :" Would your brother say that behind door B is heaven?"
or
I ask giant no1 :" Would your brother say that behind door B is hell?"
or
I ask giant no2 :" Would your brother say that behind door B is hell?"

Edited 6/18/2014 13:47:12

Yep, or "what would your brother say if i aked him where is the heaven's door?" :D

An archeologist in egypt unburies some ancient chambers. It is said that in holds either treasures or death. In the chambers he happens to find two enormous granite doors, one has the symbol of a King, the other the symbol of a snake on it.
Under the symbol of the Snake is written in glyphs: "Behind this door you will find death"
Under the symbol of the King the glyphs say: "One of the statements is true"

Which gate should the archeologist open?

Take the snake :) if the 2nd is true, the snake sentence is wrong -->he lives.
if the 2nd is wrong, both have to be wrong -->he lives again. Sorry for my bad explanation.

27. (headache garanteed)
One hundred dwarves were captured by a mean and hungry oger, but the oger wants to play with them and let them a chance to get out of his dungeon alive. He places them on a big staircase with a hundred steps, each darf with a hat on the head that can be either white or black.The dwarves are looking down, in a manner that one dwarf can only see the hats of the dwarves lower than him on the staircase.One by one, each dwarf then must announce the color of his hat, starting the dwarf on top of the staircase. If one shouts the right color he lives, if not the oger eats him immediatly. The oger, in his great clemency, allow the dwarves 5 min before starting the game to elaborate a strategy in order to save the maximum of dwarves as they can.
What would be the optimum strategy and how many dwarves would it statistically save?

Maybe i misunderstood the rules, but it didnt seem so heachachy.


They will save 99 dwarves and a 100 with a 50% chance.
First dwarf will go and say the color of the dwarf directly before him. So there is the 50% to die or live. Next dwarf will say the color he got told, but will put in some sort of delay, if that color is of the same color as the next dwarf before him or not. This way nobody else will have to die.

Edited 6/18/2014 16:12:44

#27: Define black hats as "1" and white hats as "0". Have the top dwarf count how many black hats there are and apply that number mod 2, which will be his guess.

Regardless of whether he is eaten or not, the next dwarf will know how many black hats the top dwarf saw (mod 2); since he can see every hat but his own (and the first guy's, but he doesn't matter), he should count the number of black hats he sees. If it matches (mod 2), then he has a white hat; if it doesn't match (mod 2), he has a black hat. He guesses correctly.

Everytime a dwarf (after the first one) says "Black Hat", the base guess (the one that the first dwarf said) should be flipped. Count the black hats, and again, if it matches (mod 2), then he has a white hat; if it doesn't match (mod 2), he has a black hat.

All dwarves after the first WILL guess correctly, thus 99 dwarves will always be saved. The first dwarf has a 50% chance of being saved. So, on average, 99.5 dwarves will live.

(This works if the dwarves have to go rapid-fire, and doesn't depend on wait times)

Edited 6/18/2014 16:16:55

But some overly stressed dwarves are prone to calculation errors :)

Black, no, wait white! aaaahhh

Edited 6/18/2014 16:19:50

They're also prone to panicking and not delaying properly, so I don't see the difference :)

White! Get me out of here!
(The last guy didn't delay, so...) White! *NOM NOM*

Then again assuming you only have one panicking guy both strategies can immediately go back on track with the next dwarf :3

Edited 6/18/2014 16:30:24

@myhand: the dwarves can't use any tells (the oger is watching)
@Riya: you got it^^, nice one (although more simply put, if first dwarf see an even number of white hats, he shouts white, if not he shouts black)

edit: And now starts the headache for those who don't understand the answer right away :D

Edited 6/18/2014 16:32:14

Well, if you've seen the answer for this one, it'll be easy, but why not?

#28: The king offers a knight one of his daughters as a standard hero reward for saving the kingdom. The oldest daughter always tells the truth. The middle daughter is random whether she tells the truth or not. The youngest daughter always lies. The knight doesn't know which daughter is which, and the king offers him one yes/no question to ask to only one daughter.

The knight would like to have either the oldest daughter or the youngest daughter, since he'll know where he stands with either of them - as long as he avoids the middle one, he's fine.

What question can the knight ask to ensure that he doesn't get the middle daughter?

Edited 6/18/2014 16:39:59

If i ask your sister , what your other sister would say .... / .... would she tell me if i wear a white hat or black ?

She says orange. The ogre eats you, but at least you get the door to heaven.

I want the middle daughter. Seems more like a real woman, random in telling the truth or not .

The Knight would all ( despite being terribly rude ! ) " is she older than her? "

The middle's older than the youngest, so maybe you'll satisfy myhand :D

As you can tell this knight is an idiot, so I might as well add...

With the answer to the question (can either be yes/no), who does he pick?

Edited 6/18/2014 17:28:53

does the little sister and the big sister knows is what state (lie/truth) is her middle sister right now? this is wierd because if they don't, i can ask a question like "would your middle sister tell me she is the middle sister if i were to ask her?", the little sister would answer "i don't know", but how would the big sister answer? How do you lie when you don't know the anwser?