Brain Teasers

It's all algebra. It's not fuzzy, it's quite precise.

The unknown variable is each monk's own forehead

F = monk's own forehead

D = total number of dots

The question is: Is F a subset of D?

M = total number of monks

Each monk sees (M - 1) other foreheads. (M - F)

M is a known value [in this version M = 100]

F is a known value [F = 1 in all versions]

D is an unknown value, BUT we know it is greater than 0

U = number of uninfected monks [U = M - D)

E = number of evenings

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

On the first evening, E = 1

  • If D = 1:
  • U see 1 dot (D)
  • D sees 99 uninfected monks (U)

U = M - D = 99

D = 1 = F = E

There is one dotted monk, and he knows who he is, on the first evening

- - - - - - - - - - - - - - - - - - -
On the second evening, E = 2

  • If D = 2
  • U see 2 dots (D)
  • D see 1 dot (D-1)

D both know that D is greater than 0. They also know that if D = 1 then D would have died when E = 1

Therefore, since D is greater than 0, and also greater than 1, then D must = 2

D = 2 = E = F + 1

- - - - - - - - - - - - - - - - - - - - - -

No matter what number you give to D, D will always = E

The number of dots always equals the number of evenings

F is a subset of D if E = D - 1

in other words:
If you see one less dot than the number of evenings, you know that you have a dot


:)
 
Hiiii,

Try again :( On the first evening he DOES NOT SEE 99 uninfected monks he sees 9 infected... None of the monks know they have it utnil the 10th day...

Why not just stop with the math shit and use some common sense... If there is 10 with a dot than the infected all see 9 with it and the uninfected see 10 with it...

You guys are pretty comical on this thread...
 
Quote from Te':

Hiiii,

Try again :( On the first evening he DOES NOT SEE 99 uninfected monks he sees 9 infected... None of the monks know they have it utnil the 11th day...
More...

not strictly correct. the monks that have it will know on the 10th evening. the monks that don't have it will know on the 11th.
 
Quote from daniel_m:



not strictly correct. the monks that have it will know on the 10th evening. the monks that don't have it will know on the 11th.
More...

Yes you are right -- the above is a typo, but it does not change the fact that his formula is incorrect...
 
The formula is correct. It may take a long time to figure it out, but when you do you will laugh

D = 1 means only one dot

"On the first evening, E = 1
IF D = 1:
U see 1 dot (D)
D sees 99 uninfected monks (U)"

IF there is only one, this would be the case. If there is more than one, this formula would not work, D would NOT equal E

You have to build up starting from what happens in the case that there is only 1 dot. That's the basis for understanding what happens when there is more than one dot.

Eventually you work your way up to 10

But the point is, if you see one less dot than the number of evenings, you know you have a dot.

On the first evening, IF THERE'S ONLY ONE dot, he would see 0 dots, and know he was it.
If there's two, they will both see only one dot on the second evening, and know they are the two.
If there's three, they will all see two dots on the third evening

Everyone knows from the first evening exactly how many dots they have seen. What they don't know is whether they are seeing one less than the ones with no dots. When they see one less dot than the number of evenings, then they know the answer

AND THAT'S THE SOLUTION!
 
Quote from hii a_ooiioo_a:



But the point is, if you see one less dot than the number of evenings, you know you have a dot.

On the first evening, IF THERE'S ONLY ONE dot, he would see 0 dots, and know he was it.
If there's two, they will both see only one dot on the second evening, and know they are the two.
If there's three, they will all see two dots on he third evening

Everyone knows from the first evening exactly how many dots they have seen. What they don't know is whether they are seeing one less than the ones with no dots. When they see one less dot than the number of evenings, then they know the answer
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Hiii,

Thank you so very much for letting me in on what the point is, because not knowing it has been really eating away at my brain since I gave the answer after literally only 2mins of meditating upon it...

So Fibanocci please do enlighten me as to what the 'D sees' mathematical expression is??
 
It's even funnier when you get it, and you look back at how frustrating it was, and see how frustrating it still is for those who haven't gotten it

Thanks Daniel for giving me the answer, Lobster for asking the question, and Te for making me laugh

:)
 
Quote from hii a_ooiioo_a:

It's even funnier when you get it, and you look back at how frustrating it was, and see how frustrating it still is for those who haven't gotten it

Thanks Daniel for giving me the answer, Lobster for asking the question, and Te for making me laugh

:)
More...

APPLEHEAD
 
here's another one. i got this from that site ddefina (i think) recommended.

FINALLY got it today. man this stuff is frustrating. i hate riddles!!

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?



PS - hiiiaaooo, let's just remember that commisso (Te') had this answer in like two minutes flat, and has repeatedly explained (to a certain extent) what's now been repeated ad nauseum.
the only thing we really lack is a conclusive way to prove the relationship between number of nights it takes for you to KNOW you have a dot, and the total amount of dots.
your mathematical attempt to show it fails..
 
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