Brain Teasers

[alfonso]

Brain teasers are such fun aren't they?

I really enjoyed the one about the monks. That would be one of the best I've come across.

daniel_m, the answer to your mother/son question is the mother was 84 when she died.

I have another, if people are interested.

There are two lengths of rope. Each one burns in exactly one hour after it is set alight. The two pieces of rope are not necessarily of the same length or width as each other.

They also are not of uniform width (they may be wider in middle than on the end), thus burning half of the rope does not necessarily correspond to half an hour having elapsed.

By burning the ropes, how do you measure 45 minutes worth of time?

 

[stu]

you use a stopwatch, 3 socks and a monk ?

 

[jaan]

Quote from hii a_ooiioo_a:
It's all algebra. It's not fuzzy, it's quite precise.

thanks for your proof. unfortunately, i must agree with daniel that it is not rigorous in the mathematical sense, because you made a leap of faith here:

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

i'm quite sure that this assertion is correct, but the problem is that it does not follow (in a mathematical sense) from your analysis of case1 and case2.

Quote from Lobster:
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.

*blush* thank YOU for the excellent riddle.

- jaan

 

[Te']

Quote from jaan:

thanks for your proof. unfortunately, i must agree with daniel that it is not rigorous in the mathematical sense, because you made a leap of faith here:

i'm quite sure that this assertion is correct, but the problem is that it does not follow (in a mathematical sense) from your analysis of case1 and case2.

*blush* thank YOU for the excellent riddle.

- jaan

Jann,
Why do you assume there must be a mathematical explanation for how the monks were able to know they had the disease? I am no physicist or mathematician, but I was under the impression that math really comes to show its limitations when there is a self-inferential element thrown into the mix; is it not possible that there is a logical explanation to how the monks came to know they were infected that is beyond the reach of mathematics?

If the explanation of sub-atomic particles being both destrucible and indestructible, at the same time, can escape the reach of logic; why can't the falsification of inductive logic elude the reach of mathematics?

Bet your bottom $ that these monks were well read on Hume, Popper and Mills. In fact, the study of some spectacular blow-ups in our own arena may have been enough for the monks to know how to conclude they did indeed have the dot.

Actualy that is the thing that truly amuses me about this puzzle; the ties to trading and especialy the two spectacular blow-outs of Merriwhether and Niederhoffer. The 10 monks knew and applied what they never did, whats more is that in the monk's cases, as well as LTCM and Niederhoffer, they were their own 'black swans'.

To my knowledge there is no mathematical explanation for the Epicurus Paradox, but one can 'get' it. Math is a tool we use to measure, label, and categorize reality -- IT IS NOT REALITY ITSELF, 'the map is not the territory' and 'the finger pointing at the moon is not the moon itself'; as such there will always be IMO some phonomena that eludes it and it is usually of the self-inferential nature.

At any rate one can 'get' or 'know' something without having to prove he knows it with mathematics inorder to know he knows it. It took me about 2 mins of visualizing being one of the infected to 'get' the answer to this riddle...

PEACE and good-trading,
Commisso

 

[hii a_ooiioo_a]

No, it's a mathematical deduction.

Monks were merely used to give it a human face.

The whole riddle is to pose the question "how do you calculate the equation with an unknown variable".

The unknown variable is the monk's own forehead.

 

[Te']

Quote from hii a_ooiioo_a:

No, it's a mathematical deduction.

Monks were merely used to give it a human face.

The whole riddle is to pose the question "how do you calculate the equation with an unknown variable".

The unknown variable is the monk's own forehead.

hii a_oiiou,

Perhaps there is some mathematical explanation for the riddle, but considering how you responded to this puzzle in the earlier pages of this thread, I think it would be safe for me to assume you would still be looking for the answer with your mathematical intricate formulas if I hadn't spoon fed the answer to the forum -- that i mind you came from a tool other than your mathematics...

All you did was take my answer that came to me in two minutes and spent hours by your own admission trying to fit it into some pretty little mathematical box, one in which i mind you is not even remotely close to the solution...

mathematics is indeed a clever tool, but it is not the only tool and I can assure you that it is not always the best one either...

We often spend far too much time building a bridge, to get from one side to the other, without ever taking the time to realize the stream we are attempting to cross is only 1 foot deep...

 

[hii a_ooiioo_a]

Quote from Te':
Perhaps there is some mathematical explanation for the riddle, but considering how you responded to this puzzle in the earlier pages of this thread, I think it would be safe for me to assume you would still be looking for the answer with your mathematical intricate formulas if I hadn't spoon fed the answer to the forum -- that i mind you came from a tool other than your mathematics...

Wrong assumption.

If Daniel had not given the explanation to this puzzle, I would have gone on assuming that the monks would never kill themselves because I thought they would never discover if they had the dot or not.

It was only when I tried to explain the solution to Goldenarm that I began to see the mathematics of it.
If I were more of a mathematician, I would have seen it right away when Jaan gave the formula. But I had to work it out step by step all the way from step one.

 

[stu]

It is satisfying and necessary to see and understand logical mathematical representation rather than a guess or an "I just knew explanation". It is impressive when both are displayed. First come up with the inductive reasoning by all means but then follow up by expressing the answer with the sophistication mathematics allows. Both may be necessary to get to an eventual answer in a multi faceted problem. One could be a guess or based on previous knowledge the other has to agree with a known discipline which in the end must stand up to proper scrutiny.

 

[Te']

Quote from stu:

It is satisfying and necessary to see and understand logical mathematical representation rather than a guess or an "I just knew explanation". It is impressive when both are displayed. First come up with the inductive reasoning by all means but then follow up by expressing the answer with the sophistication mathematics allows. Both may be necessary to get to an eventual answer in a multi faceted problem. One could be a guess or based on previous knowledge the other has to agree with a known discipline which in the end must stand up to proper scrutiny.

I don't neccesarily disagree with the above statement, but I think you may be mistaking logic for a guess...

 

[jaan]

Quote from Te':
I am no physicist or mathematician, but I was under the impression that math really comes to show its limitations when there is a self-inferential element thrown into the mix;

correct -- and even worse if infinity gets involved...

i'm well aware that there are mathematically well defined problems whose solution is beyond the limits of mathematics. see gödel's theorem for example.

not to mention all the problems that cannot be formulated in math terms in the first place.

that said i don't think the monks' puzzle is one of those. hii a_ooiioo_a basically provided a proof with a hole. i'm pretty sure that i could plug that hole in a couple of hours. however, the resulting proof is probably not going to be an easy read, so it would not really convince anybody but the mathematicians here.

If the explanation of sub-atomic particles being both destrucible and indestructible, at the same time, can escape the reach of logic; why can't the falsification of inductive logic elude the reach of mathematics?

ugh... let's just say that answering this would prompt a thread-length prediciton from nitro in like 2 seconds...

At any rate one can 'get' or 'know' something without having to prove he knows it with mathematics inorder to know he knows it. It took me about 2 mins of visualizing being one of the infected to 'get' the answer to this riddle...

absolutely! however, the problem with our intuition is that it is known to play tricks on us. did you see the "monty hall problem" mentioned by aphie? here it is:

http://www.google.com/search?q=monty+hall+problem

now there's a problem that definitely beat my intuition!

- jaan