Brain Teasers

Quote from 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?
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Without reading the rest of the thread, a heart.
 
Quote from jaan:


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
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Thanks for the response and I will check out the Monty Hall Problem :)

PEACE and good-trading,
Commisso
 
Re: the monk riddle.

I think it can be proven that the number of days required to know, conclusively, that one has a dot on one's forehead is the same as the total number of dots. Such a proof doesn't have to be 'mathematical' or algebraic. In fact, I can't see how it could be stated in terms of only numbers, as numbers don't 'realize' anything - realization being a key element of this riddle.

The proof could be given logically in another form however. Like a syllogism, for example. I can't seem to come up with anything though.

No takers on the rope problem?
 
Quote from alfonso:

Re: the monk riddle.

I think it can be proven that the number of days required to know, conclusively, that one has a dot on one's forehead is the same as the total number of dots. Such a proof doesn't have to be 'mathematical' or algebraic. In fact, I can't see how it could be stated in terms of only numbers, as numbers don't 'realize' anything - realization being a key element of this riddle.

The proof could be given logically in another form however. Like a syllogism, for example. I can't seem to come up with anything though.

No takers on the rope problem?
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The monks used falsification to induce they had a dot. They could not infer that there were only 9 with the dot, because their fore-head could not be seen which left still an unknown element, but day 10 was enough to refute the claim that there were only 9. Once the monks could refute the inference that there were only 9 infected, they need only to look around the room for the 10th and conclude they were indeed the mark. If you look around the table and cannot spot the mark then you are it.

They just built an inference based on inductive logic and then falsified the inference using the 10th day as their black swan.

These monks were well edumacated :D

PEACE and good-trading,
Commisso
 
Quote from alfonso:
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?
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Fact 1
If we ignite each end of one rope, it will burn for 30 minutes.

Fact 2
If we take a rope which has been ignited on one end and which has been burning for 30 minutes, and then ignite the other end, it will burn for an additional 15 minutes.

Solution
Simultaneously ignite the first rope from both ends and the second rope from one end only. When the first rope has burned (30 minutes), ignite the other end of the second rope. When the second rope has burned (15 minutes), a total of 45 minutes will have elapsed.
 
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