Brain Teasers

[daniel_m]

when only one person has the dot, it takes one night for this to be realised. that night, he kills himself.

when two people have the dot, it takes two nights.
the first night, A will see only B's dot, and B will see only A's dot.
when they both come back the next night,
A will realise that B must be seeing a dot on A's head, (and no one else's)
B will realise that A must be seeing a dot on B's head. (and no one else's.)

that night they both kill themselves.

when three people have the dot, it takes three nights.

the first night, A sees a dot on B's and C's heads, B sees a dot on A's and C's and C sees a dot on A's and B's.

the second night,
A thinks that B thought only C had the dot, or that C thought that only B had the dot.
B thinks that A thought only C had the dot, or that C thought only A had the dot.
C thinks that A thought only B had the dot, or that B thought only A had the dot.

the third night,
A realises that B and C must be also seeing a dot on A
B realises that A and C must be also seeing a dot on B
C realises that A and C must be also seeing a dot on C

that night they all kill themselves.

with FOUR people, it takes four nights and so on.

the point is, the ones with the dots will never realise they have one until the same numbered night as there are dots comes up.


On the tenth night, the 10 people with the dots will realise that they each have a dot and take their lives that night.

 

[hii a_ooiioo_a]

Thank you


I'm now going to look in the mirror, and if I see a red dot on my forehead I am going to kill myself.

 

[Gordon Gekko]

Quote from hii a_ooiioo_a:

I'm now going to look in the mirror, and if I see a red dot on my forehead I am going to kill myself.

me too

 

[stu]

Quote from Aaron:

Is that the one...

"You have a mixture of red and white socks in a bag. What is the minimum number of socks you would have to pull out to be sure of getting a matching pair?"

[This looks like a "chit chat" forum thread.]

the answer is 6 socks

(but I don't know why)

 

[aphexcoil]

To be gold is to be good;
To be stone is to be nothing;
To be glass is to be fragile;
To be cold is to be cruel.
Unmetaphored, what am I?

 

[goldenarm]

Quote from daniel_m:

when only one person has the dot, it takes one night for this to be realised. that night, he kills himself.

when two people have the dot, it takes two nights.
the first night, A will see only B's dot, and B will see only A's dot.
when they both come back the next night,
A will realise that B must be seeing a dot on A's head, (and no one else's)
B will realise that A must be seeing a dot on B's head. (and no one else's.)

that night they both kill themselves.

when three people have the dot, it takes three nights.

the first night, A sees a dot on B's and C's heads, B sees a dot on A's and C's and C sees a dot on A's and B's.

the second night,
A thinks that B thought only C had the dot, or that C thought that only B had the dot.
B thinks that A thought only C had the dot, or that C thought only A had the dot.
C thinks that A thought only B had the dot, or that B thought only A had the dot.

the third night,
A realises that B and C must be also seeing a dot on A
B realises that A and C must be also seeing a dot on B
C realises that A and C must be also seeing a dot on C

that night they all kill themselves.

with FOUR people, it takes four nights and so on.

the point is, the ones with the dots will never realise they have one until the same numbered night as there are dots comes up.


On the tenth night, the 10 people with the dots will realise that they each have a dot and take their lives that night.

No wonder it's hard to argue with you. This is the stupidest solution I ever heard.

If the monks don't know the total number of infected people, then they will not kill themselves based on the number of dots they see. If I'm infected and I see 9 dots, I won't automatically kill myself. Only a moron would do that. This riddle is not a riddle because it is not valid. The monks HAVE to know the total number of infected monks for this riddle to work, and even then it would only take ONE day, not TEN.

It would take ten days, ONLY if one infected monk killed himself each night. Then by process of elimination, the last infected monk would kill himself on the tenth night. BUT this requires everyone to know that there are TEN infected monks and it assumes the monks would kill themselves off sequentially, which is NOT true. I mean, after the first night, you'd know if you were the tenth infected monk! The riddle was told incorrectly.

You've wasted your single brain cell on this pointless exercise! Joke's on you, ha ha ha!

 

[goldenarm]

Actually, I have an answer to the monk riddle. The diseased monks were reluctant to kill themselves over the first nine days until they began to feel the symptoms of the disease on the tenth day. Due to the excruciating pain, they killed themselves on the last day.

PUZZLE SOLVED! GIVE THE MAN A GOLD STAR!

 

[aphexcoil]

Quote from goldenarm:

BUT this requires everyone to know that there are TEN infected

This is incorrect.

 

[goldenarm]

Thanks for the enlightening response, Aphie.

 

[jaan]

Quote from daniel_m:
then lobster came up with some crap about a maths professor not understanding it

i think you may have jumped lobster unnecessarily here. he said that the pofessor was puzzled about the information theory aspects of the puzzle, not just the puzzle itself.

to me the monks' puzzle sounds like a variant of the famous "three hat problem":

http://www.google.com/search?q=three+hat+problem

the THP caused a huge splash in the math community, being a seemingly simple puzzle yet challenging the very foundations of modern information theory.

as far as the explanation to the monks' puzzle is concerned, let me try to give a shot as well (in know i'm repeating others, just trying to give it another form):

1. there are N infected monks (the number is NOT known in advance);

2. infected monks see N-1 spots, the ones that are not infected see N spots;

3. the monks get the one bit of information of whether they are infected or not by comparing the number of spots they see on others to the number of days that have passed. hence:

4. on the N-th day it becomes clear to all infected monks that they are infected, because the number of days (N) is bigger than the number of spots they see (N-1). which effectively sends a message to infected monks that others have been returning thanks to his spot. bummer...

- jaan