Brain Teasers

[hii a_ooiioo_a]

Failed? How?
It may not be the absolute best mathematical formula, but it's very nearly there at least. It's well on the way

And really, my final assessment is the answer: If you have one less dot than the number of days, then you know you have a dot. This is because the unknown variable is whether you see the same amount of dots as the undotted ones, or whether you see one less

If you see (E - 1) dots, it's you.

 

[daniel_m]

yes, that's the answer, but how can we KNOW that is the answer?

i said your proof fails because you have D = number of dots, and then you have the statement, "D sees". that's just nonsensical.

 

[hii a_ooiioo_a]

A woman spends one-sixth of her life in childhood, one-twelfth in youth, and one-seventh as a single woman. Five years after she got married, a son was born who died four years before his mother at half his mothers final age. what was her final age?

S = son's final age
M = mother's final age
C = childhood
Y = youth
U = singlehood
W = age at marriage

6C = 12Y = 7U = 2S = M
C = 2Y
W+5 + S + 4 = M
C + Y + U = W
S = W + 9
S = C + Y + U + 9
S = 3Y + U + 9
W = 3Y + U
2W + 18 = M
2W + 18 =
W + 9 = 6Y = S
6Y = 3Y + U + 9
U + 9 = 3Y
2U + 9 = W
2U + 9 = S - 9
2U + 18 = S
9 = 3Y - U
36 = 12Y - 4U
36 = 7U - 4U = 3U
U = 12
6Y = 3Y + 21
Y = 7
The woman died at 84
Childhood = 14
Youth = 14 to 21
Single = 21 to 33
Son born when 38
Son dies age 42, when she is 80
She dies age 84

 

[hii a_ooiioo_a]

Quote from daniel_m:

I said your proof fails because you have D = number of dots, and then you have the statement, "D sees". that's just nonsensical.

D is the number of dots, equally expressed as the number of monks with dots

 

[aphexcoil]

Quote from Te':

If you can understand that, it wil go a long way toward understanding why traders such as Niedrhoffer and LTCM blew up...

Red dots on monks head for a cute puzzle and the reason LTCM "blew up" are two totally different things. When are you going to visit us in our world and stop meandering in your "yoga-hippy-happy" fantasy land?

 

[Lobster]

Quote from jaan:

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

Thank you so much for your post. ET seems to have some very good people. Maybe Baron should apply for a license to award PhDs to members.

 

[Lobster]

Quote from jaan:


the only proper proof i can imagine would use mathematical induction -- ie stating that the theorem holds for N=1, and proving that for each N that the theorem holds, it would also hold for N1=N+1. but the proof would definitely not be trivial not to mention intuitive.

- jaan

Actually, it is not even trivial to state the conjecture that we are trying to prove. I think what we would need to prove is

1. The above algorithm works if every monk knows he has to apply it.

2. There is no algorithm that the monks could apply that would let them find the solution earlier than after N days.

Of course, we always assume that all the monks are perfectly logical and intelligent. I forgot to state that in the very beginning, since it is kind of obvious that we want to analyze only that case.

 

[Te']

Quote from aphexcoil:



Red dots on monks head for a cute puzzle and the reason LTCM "blew up" are two totally different things. When are you going to visit us in our world and stop meandering in your "yoga-hippy-happy" fantasy land?

ur right Aphie I'm a babbling idiot...

 

[Te']

Quote from aphexcoil:



Red dots on monks head for a cute puzzle and the reason LTCM "blew up" are two totally different things. When are you going to visit us in our world and stop meandering in your "yoga-hippy-happy" fantasy land?

Follow the swans APPLEHEAD, perhaps you may just learn something...

 

[stu]

5 socks then ?