Conundrums, Puzzles, Logic Problems (1 Viewer)

[The Man from Laramie]

by the way, how do you do the :spoiler: tag?

[spoiler]text[/spoiler]

 

[Mungo Burrows]

by the way, how do you do the :spoiler: tag?

[spoiler] Hide Me [/spoiler] or...

 

[SkyRattlers]

You must use each digit from 1-9 only once, solve:

  * *
x   *
-----
  * *
+ * *
-----
  * *

 

[Sweet J]

There are two lengths of rope.

Each one can burn in exactly one hour.

They are not necessarily of the same length or width as each other.

They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

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

Off the top of my head:I'd light both ends of one rope (1/2 hour). When that is done, I'd cut the other rope in 1/2, then light both ends of each of the pieces (15 min)

Wow. Impressive.My answer was going to be to use a watch.

Cutting the second rope in half won't necessarily equal 15 minutes, though, because they aren't uniform width. The second rope may have one half burning faster than the other... lighting the halves could burn each half out in 10 and 20 minutes, for example.

He was really close. You don't need to cut it in half. You light both ends of rope 1 and one end of rope 2. When rope 1 burns out, you light the other end of rope 2. Regardless or non-uniformity in the thickness, it will burn out in exactly 45 minutes.

A agree that your answer is correct, but I still think I was right:We can all agree that lighting the first rope at both ends = 1/2 hour, correct?

If so, why can't the same principles apply to the second rope? You cut the second rope in half, and you light all four ends (both ends of each 1/2 piece). The same principles apply to equal 1/4 hour (15 min.)

What if the two halfs are not uniform? One could burn twice as fast as the other.

Ah, I see what you and dragons are saying.

 

[Buckychudd]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

mytagid = Math.floor( Math.random() * 100 );document.write("Sounds good to me. If after 1 day, 1 dragon saw 98 pairs of, say, blue eyes, he'd know he was the one with red eyes, and die. This didn't happen. So the dragons know that there are at least 2 dragons with red eyes. On day 2, if a dragon saw 97 blue eyed dragons and 1 red eyed dragon, he'd know he was the other red eyed dragon and die. This didn't happen, so they know there must be at least 3 dragons with red eyes. Repeat.

*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

mytagid = Math.floor( Math.random() * 100 );document.write("actually, the dragons know that there are at least 98 other dragons on the island with red eyes. they can see them. look at it as if there are two dragons on the island. they both have red eyes. when the logician appears and says "at least one of you MFers has red eyes" each dragon assumes it's the other dragon that has red eyes and assume that they themselves have blue eyes. if it is true that one of those dragons had blue eyes, then the other dragon would see those blue eyes and know he has red eyes, then he'd be dead the next day...

but, both dragons have red eyes, and they can see the other has red eyes. therefore, when neither of them dies on the first day, it is impossible that either of the dragons have blue eyes, because neither of them died. so they both die.

now, just extrapolate that out with 99 dragons.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

 

[Sweet J]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.By the way, for the dragon question, do we really need the spoiler tag? It just confuses things.

 

[jonessed]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

 

[Sweet J]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Part of the question has got to be missing.

 

[parasaurolophus]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Part of the question has got to be missing.

it is.you are allowed to go only once

 

[Desert_Power]

You must use each digit from 0-9 only once, solve:

* *x   *-----  * *+ * *-----  * *

how can you use ten digits if there are 9 possible places for them?

 

[Blind Tiger]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Part of the question has got to be missing.

it is.you are allowed to go only once

 

[jobooskin]

You must use each digit from 0-9 only once, solve:

   17X  4

68

+ 25

93

 

[SoCalBroncoFan]

You must use each digit from 0-9 only once, solve:

* *x   *-----  * *+ * *-----  * *

how can you use ten digits if there are 9 possible places for them?

084326597Close enough.

 

[SkyRattlers]

You must use each digit from 0-9 only once, solve:

* *x   *-----  * *+ * *-----  * *

how can you use ten digits if there are 9 possible places for them?

My mistake. 0 isn't used. Should just be 1-9. Looks like someone solved it anyway though.

 

[Peyton Marino]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

 

[shadyridr]

What does -5^2=?

 

[TheIronSheik]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Flip the switches and look through the doorway into the other room.

 

[Mungo Burrows]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.

 

[The Man from Laramie]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Flip the switches and look through the doorway into the other room.

 

[The Man from Laramie]

You must use each digit from 0-9 only once, solve:

   17X  4

68

+ 25

93

[/QUOTE]Did you deduce this, or was it a guess that worked?

 

[TheIronSheik]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Flip the switches and look through the doorway into the other room.

Doing it my way saves you 4 minutes and 50 seconds.

 

[fatguyinalittlecoat]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.

:(

The explanations so far have been sorely lacking. You guys are right to be skeptical.

 

[Peyton Marino]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.

:(

The explanations so far have been sorely lacking. You guys are right to be skeptical.

this is originally how i explained it to one of my friends, and he told me I was right.now i've re-examined the situation with >2 dragons and it doesn't make any sense.

 

[Mungo Burrows]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.

 

[Buckychudd]

Can we change the title of the thread to "Half finished logic problems that make no sense and have no real solutions".

TIA

 

[Peyton Marino]

While I see how this would work with 2 dragons, I don't see how it would work with 99 dragons.

I agree that I don't see it.

 

[(HULK)]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

mytagid = Math.floor( Math.random() * 100 );document.write("Sounds good to me. If after 1 day, 1 dragon saw 98 pairs of, say, blue eyes, he'd know he was the one with red eyes, and die. This didn't happen. So the dragons know that there are at least 2 dragons with red eyes. On day 2, if a dragon saw 97 blue eyed dragons and 1 red eyed dragon, he'd know he was the other red eyed dragon and die. This didn't happen, so they know there must be at least 3 dragons with red eyes. Repeat.

*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

mytagid = Math.floor( Math.random() * 100 );document.write("actually, the dragons know that there are at least 98 other dragons on the island with red eyes. they can see them. look at it as if there are two dragons on the island. they both have red eyes. when the logician appears and says "at least one of you MFers has red eyes" each dragon assumes it's the other dragon that has red eyes and assume that they themselves have blue eyes. if it is true that one of those dragons had blue eyes, then the other dragon would see those blue eyes and know he has red eyes, then he'd be dead the next day...

but, both dragons have red eyes, and they can see the other has red eyes. therefore, when neither of them dies on the first day, it is impossible that either of the dragons have blue eyes, because neither of them died. so they both die.

now, just extrapolate that out with 99 dragons.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

This doesn't make any sense at all.For starters, where was it stated that a dragon must have either red or blue eyes? Why couldn't his eyes be any other color?

 

[Peyton Marino]

Can we change the title of the thread to "Half finished logic problems that make no sense and have no real solutions".TIA

listen assbag, i spent the better part of a week trying to figure this thing out. what have you spent? 10 minutes? btfu.

 

[Peyton Marino]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

mytagid = Math.floor( Math.random() * 100 );document.write("Sounds good to me. If after 1 day, 1 dragon saw 98 pairs of, say, blue eyes, he'd know he was the one with red eyes, and die. This didn't happen. So the dragons know that there are at least 2 dragons with red eyes. On day 2, if a dragon saw 97 blue eyed dragons and 1 red eyed dragon, he'd know he was the other red eyed dragon and die. This didn't happen, so they know there must be at least 3 dragons with red eyes. Repeat.

*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

mytagid = Math.floor( Math.random() * 100 );document.write("actually, the dragons know that there are at least 98 other dragons on the island with red eyes. they can see them. look at it as if there are two dragons on the island. they both have red eyes. when the logician appears and says "at least one of you MFers has red eyes" each dragon assumes it's the other dragon that has red eyes and assume that they themselves have blue eyes. if it is true that one of those dragons had blue eyes, then the other dragon would see those blue eyes and know he has red eyes, then he'd be dead the next day...

but, both dragons have red eyes, and they can see the other has red eyes. therefore, when neither of them dies on the first day, it is impossible that either of the dragons have blue eyes, because neither of them died. so they both die.

now, just extrapolate that out with 99 dragons.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

This doesn't make any sense at all.For starters, where was it stated that a dragon must have either red or blue eyes? Why couldn't his eyes be any other color?

they all have red eyes. that was stated in the second or third sentence of the original problem. and yes, i've already conceded that my answer doesn't work. welcome.

 

[(HULK)]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

 

[(HULK)]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

mytagid = Math.floor( Math.random() * 100 );document.write("Sounds good to me. If after 1 day, 1 dragon saw 98 pairs of, say, blue eyes, he'd know he was the one with red eyes, and die. This didn't happen. So the dragons know that there are at least 2 dragons with red eyes. On day 2, if a dragon saw 97 blue eyed dragons and 1 red eyed dragon, he'd know he was the other red eyed dragon and die. This didn't happen, so they know there must be at least 3 dragons with red eyes. Repeat.

*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

mytagid = Math.floor( Math.random() * 100 );document.write("actually, the dragons know that there are at least 98 other dragons on the island with red eyes. they can see them. look at it as if there are two dragons on the island. they both have red eyes. when the logician appears and says "at least one of you MFers has red eyes" each dragon assumes it's the other dragon that has red eyes and assume that they themselves have blue eyes. if it is true that one of those dragons had blue eyes, then the other dragon would see those blue eyes and know he has red eyes, then he'd be dead the next day...

but, both dragons have red eyes, and they can see the other has red eyes. therefore, when neither of them dies on the first day, it is impossible that either of the dragons have blue eyes, because neither of them died. so they both die.

now, just extrapolate that out with 99 dragons.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

This doesn't make any sense at all.For starters, where was it stated that a dragon must have either red or blue eyes? Why couldn't his eyes be any other color?

they all have red eyes. that was stated in the second or third sentence of the original problem. and yes, i've already conceded that my answer doesn't work. welcome.

Are you sure the logician didn't say that there is at least 1 dragon with BLUE eyes?

 

[Peyton Marino]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

 

[Peyton Marino]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

mytagid = Math.floor( Math.random() * 100 );document.write("Sounds good to me. If after 1 day, 1 dragon saw 98 pairs of, say, blue eyes, he'd know he was the one with red eyes, and die. This didn't happen. So the dragons know that there are at least 2 dragons with red eyes. On day 2, if a dragon saw 97 blue eyed dragons and 1 red eyed dragon, he'd know he was the other red eyed dragon and die. This didn't happen, so they know there must be at least 3 dragons with red eyes. Repeat.

*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

mytagid = Math.floor( Math.random() * 100 );document.write("actually, the dragons know that there are at least 98 other dragons on the island with red eyes. they can see them. look at it as if there are two dragons on the island. they both have red eyes. when the logician appears and says "at least one of you MFers has red eyes" each dragon assumes it's the other dragon that has red eyes and assume that they themselves have blue eyes. if it is true that one of those dragons had blue eyes, then the other dragon would see those blue eyes and know he has red eyes, then he'd be dead the next day...

but, both dragons have red eyes, and they can see the other has red eyes. therefore, when neither of them dies on the first day, it is impossible that either of the dragons have blue eyes, because neither of them died. so they both die.

now, just extrapolate that out with 99 dragons.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***

");document.close();

This doesn't make any sense at all.For starters, where was it stated that a dragon must have either red or blue eyes? Why couldn't his eyes be any other color?

they all have red eyes. that was stated in the second or third sentence of the original problem. and yes, i've already conceded that my answer doesn't work. welcome.

Are you sure the logician didn't say that there is at least 1 dragon with BLUE eyes?

no, that is the question as i heard it from my friend.

 

[(HULK)]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

The answer is that you framed the riddle totally wrong.Here it is in its correct glory:

The Problem

Three dragons are living on an island. On this island, dragons either have red eyes or blue eyes. If a dragon with red eyes realizes that he has red eyes, then he will die at midnight that night. There are no reflective surfaces on the island (i.e. there is no way for a dragon to see his own eye-colour). The three dragons never speak or communicate to each other in any way, but they do see each other everyday. Thus each dragon knows the eye-colour of the other two dragons. It turns out that all three dragons on this island have red eyes.

Many years pass without a dragon dying, because no dragon ever finds out his own eye-colour. One day, a cackling wizard appears in front of all three dragons and makes the statement, "At least one of you has red eyes!", and then disappears. The dragons know that the wizard never lies.

On the n-th night since the wizard appeared, all three dragons died. What is n, and how did the dragons realize that they had red eyes?

And the answer:

Spoiler

The Solution

I could give the solution for three dragons only, by breaking the situation down into four cases and handling each case; but I will do it a better, more elegant way. I will generalize this to any number of dragons, some with red eyes and some with blue.

Let the island have n > 0 dragons with red eyes, and m dragons with blue eyes. I claim that all n dragons with red eyes will die on the n-th night after the wizard makes the statement "At least one of you has red eyes." (So for the original problem, the answer is the 3rd night). I prove this using mathematical induction on n.

If n = 1, then the lone dragon with red eyes will look around the island and see that all other dragons have blue eyes. He concludes that he is the only one with red eyes, and thus dies on the first night.

Suppose that for n = k-1, k > 1, that all k-1 red-eyed dragons die on the (k-1)-th night. Then for n = k, this is what happens: each of the k dragons will look around and see that there are k-1 dragons with red eyes on the island. Each dragon thinks, "I don't want to die, so let's assume that I have blue eyes." Then each dragon should expect the other k-1 dragons to die in the (k-1)-th night; so they wait. On the k-th day, each dragon sees that the other k-1 dragons are still alive, and thus their initial assumption that "I have blue eyes" must be false. Thus each of the k dragons realize that they have red eyes, and die on the k-th night.

 

[Buckychudd]

Can we change the title of the thread to "Half finished logic problems that make no sense and have no real solutions".TIA

listen assbag, i spent the better part of a week trying to figure this thing out. what have you spent? 10 minutes? btfu.

Ok everybody, dogpile on Peyton Marino!

 

[Peyton Marino]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

The answer is that you framed the riddle totally wrong.Here it is in its correct glory:

The Problem

Three dragons are living on an island. On this island, dragons either have red eyes or blue eyes. If a dragon with red eyes realizes that he has red eyes, then he will die at midnight that night. There are no reflective surfaces on the island (i.e. there is no way for a dragon to see his own eye-colour). The three dragons never speak or communicate to each other in any way, but they do see each other everyday. Thus each dragon knows the eye-colour of the other two dragons. It turns out that all three dragons on this island have red eyes.

Many years pass without a dragon dying, because no dragon ever finds out his own eye-colour. One day, a cackling wizard appears in front of all three dragons and makes the statement, "At least one of you has red eyes!", and then disappears. The dragons know that the wizard never lies.

On the n-th night since the wizard appeared, all three dragons died. What is n, and how did the dragons realize that they had red eyes?

And the answer:

Spoiler

The Solution

I could give the solution for three dragons only, by breaking the situation down into four cases and handling each case; but I will do it a better, more elegant way. I will generalize this to any number of dragons, some with red eyes and some with blue.

Let the island have n > 0 dragons with red eyes, and m dragons with blue eyes. I claim that all n dragons with red eyes will die on the n-th night after the wizard makes the statement "At least one of you has red eyes." (So for the original problem, the answer is the 3rd night). I prove this using mathematical induction on n.

If n = 1, then the lone dragon with red eyes will look around the island and see that all other dragons have blue eyes. He concludes that he is the only one with red eyes, and thus dies on the first night.

Suppose that for n = k-1, k > 1, that all k-1 red-eyed dragons die on the (k-1)-th night. Then for n = k, this is what happens: each of the k dragons will look around and see that there are k-1 dragons with red eyes on the island. Each dragon thinks, "I don't want to die, so let's assume that I have blue eyes." Then each dragon should expect the other k-1 dragons to die in the (k-1)-th night; so they wait. On the k-th day, each dragon sees that the other k-1 dragons are still alive, and thus their initial assumption that "I have blue eyes" must be false. Thus each of the k dragons realize that they have red eyes, and die on the k-th night.

you found this on some dude's blog.

 

[The Man from Laramie]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

 

[Alias]

http://img124.imageshack.us/my.php?image=trigridzc2.gif

Explain this one.

This was a good one, had to look up the answer to confirm my suspicions.mytagid = Math.floor( Math.random() * 100 );document.write("

you are not looking at a triangle but rather a 4 sided object, the extra space covered in the second diagram makes up for the additional space missing in the first diagram (by a total of 1 square).

You can verify this by seeing how the hypotenuse does not cross the same intersections of the endpoints of each of the smaller triangles.*** SPOILER ALERT! Click this link to display the potential spoiler text in this box. ***");document.close();

 

[(HULK)]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

Not mine. 100% culled from the internet.I felt the need to google this as I realized the question wasn't correct in the riddle. The initial riddle had no logical explaination.

 

[Peyton Marino]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

it's not hulk's explaination.

 

[The Man from Laramie]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

Not mine. 100% culled from the internet.I felt the need to google this as I realized the question wasn't correct in the riddle. The initial riddle had no logical explaination.

I applaud (Hulk)'s honesty, but don't condone (Hulk)'s deception.

 

[Peyton Marino]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

Not mine. 100% culled from the internet.I felt the need to google this as I realized the question wasn't correct in the riddle. The initial riddle had no logical explaination.

the guy's question is the same as mine except in his riddle there's only 3 dragons and you have to find N and explain how, other than already being given N and explaining how.and, I know i'm going to catch a ton of flack from all the math wizards here, but when I was trying to answer this a while ago, i too found this guy's blog and it didn't help me. I honestly can't make two ####s out of what he's saying.

 

[(HULK)]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

Not mine. 100% culled from the internet.I felt the need to google this as I realized the question wasn't correct in the riddle. The initial riddle had no logical explaination.

I applaud (Hulk)'s honesty, but don't condone (Hulk)'s deception.

I had no intention to deceive. I had to go to the innerwebs for the riddle in its correct form, the solution was also there so I posted both. I made no claim to it being mine.

 

[(HULK)]

I applaud (Hulk)'s proof by induction. Full points for nerditude.

Not mine. 100% culled from the internet.I felt the need to google this as I realized the question wasn't correct in the riddle. The initial riddle had no logical explaination.

the guy's question is the same as mine except in his riddle there's only 3 dragons and you have to find N and explain how, other than already being given N and explaining how.and, I know i'm going to catch a ton of flack from all the math wizards here, but when I was trying to answer this a while ago, i too found this guy's blog and it didn't help me. I honestly can't make two ####s out of what he's saying.

The fact that dragon's eyes can only be blue or red makes a difference, you didn't include it in your riddle.

 

[Buckychudd]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

The answer is that you framed the riddle totally wrong.Here it is in its correct glory:

The Problem

Three dragons are living on an island. On this island, dragons either have red eyes or blue eyes. If a dragon with red eyes realizes that he has red eyes, then he will die at midnight that night. There are no reflective surfaces on the island (i.e. there is no way for a dragon to see his own eye-colour). The three dragons never speak or communicate to each other in any way, but they do see each other everyday. Thus each dragon knows the eye-colour of the other two dragons. It turns out that all three dragons on this island have red eyes.

Many years pass without a dragon dying, because no dragon ever finds out his own eye-colour. One day, a cackling wizard appears in front of all three dragons and makes the statement, "At least one of you has red eyes!", and then disappears. The dragons know that the wizard never lies.

On the n-th night since the wizard appeared, all three dragons died. What is n, and how did the dragons realize that they had red eyes?

And the answer:

Spoiler

The Solution

I could give the solution for three dragons only, by breaking the situation down into four cases and handling each case; but I will do it a better, more elegant way. I will generalize this to any number of dragons, some with red eyes and some with blue.

Let the island have n > 0 dragons with red eyes, and m dragons with blue eyes. I claim that all n dragons with red eyes will die on the n-th night after the wizard makes the statement "At least one of you has red eyes." (So for the original problem, the answer is the 3rd night). I prove this using mathematical induction on n.

If n = 1, then the lone dragon with red eyes will look around the island and see that all other dragons have blue eyes. He concludes that he is the only one with red eyes, and thus dies on the first night.

Suppose that for n = k-1, k > 1, that all k-1 red-eyed dragons die on the (k-1)-th night. Then for n = k, this is what happens: each of the k dragons will look around and see that there are k-1 dragons with red eyes on the island. Each dragon thinks, "I don't want to die, so let's assume that I have blue eyes." Then each dragon should expect the other k-1 dragons to die in the (k-1)-th night; so they wait. On the k-th day, each dragon sees that the other k-1 dragons are still alive, and thus their initial assumption that "I have blue eyes" must be false. Thus each of the k dragons realize that they have red eyes, and die on the k-th night.

Either I'm stuipider than I thought, or this still doesn't make any sense.

 

[Peyton Marino]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

The answer is that you framed the riddle totally wrong.Here it is in its correct glory:

The Problem

Three dragons are living on an island. On this island, dragons either have red eyes or blue eyes. If a dragon with red eyes realizes that he has red eyes, then he will die at midnight that night. There are no reflective surfaces on the island (i.e. there is no way for a dragon to see his own eye-colour). The three dragons never speak or communicate to each other in any way, but they do see each other everyday. Thus each dragon knows the eye-colour of the other two dragons. It turns out that all three dragons on this island have red eyes.

Many years pass without a dragon dying, because no dragon ever finds out his own eye-colour. One day, a cackling wizard appears in front of all three dragons and makes the statement, "At least one of you has red eyes!", and then disappears. The dragons know that the wizard never lies.

On the n-th night since the wizard appeared, all three dragons died. What is n, and how did the dragons realize that they had red eyes?

And the answer:

Spoiler

The Solution

I could give the solution for three dragons only, by breaking the situation down into four cases and handling each case; but I will do it a better, more elegant way. I will generalize this to any number of dragons, some with red eyes and some with blue.

Let the island have n > 0 dragons with red eyes, and m dragons with blue eyes. I claim that all n dragons with red eyes will die on the n-th night after the wizard makes the statement "At least one of you has red eyes." (So for the original problem, the answer is the 3rd night). I prove this using mathematical induction on n.

If n = 1, then the lone dragon with red eyes will look around the island and see that all other dragons have blue eyes. He concludes that he is the only one with red eyes, and thus dies on the first night.

Suppose that for n = k-1, k > 1, that all k-1 red-eyed dragons die on the (k-1)-th night. Then for n = k, this is what happens: each of the k dragons will look around and see that there are k-1 dragons with red eyes on the island. Each dragon thinks, "I don't want to die, so let's assume that I have blue eyes." Then each dragon should expect the other k-1 dragons to die in the (k-1)-th night; so they wait. On the k-th day, each dragon sees that the other k-1 dragons are still alive, and thus their initial assumption that "I have blue eyes" must be false. Thus each of the k dragons realize that they have red eyes, and die on the k-th night.

Either I'm stuipider than I thought, or this still doesn't make any sense. fatguy, can you put us out of our misery?

 

[jonessed]

I got this in an interview once:

There are two rooms, one room has three light switches and the other has three bulbs. How do you determine which switch goes to which bulb without going into the second room?

I was an engineer at the time so my first instinct was to short out a bulb, but they said I couldn't damage anything.

Maybe this is an old one, I don't know. I just remember it because it came in an interview and I didn't expect it.

Part of the question has got to be missing.

it is.you are allowed to go only once

Yeah sorry. Forgot that part.

 

[Buckychudd]

there's a magical island that is populated by 99 dragons. all of these dragons have red eyes, but they do not know this. if at any time it is possible for a dragon to deduce his eye color, the dragon will die the next day at noon. dragons, being the intelligent creatures they are, never discuss eye colors and they avoid looking in water where they might accidentally see their reflection. dragons are also extremely observant, so each dragon knows that the other 98 have red eyes. one day, an evil logician appears on the island and gathers the dragons together. he yells to them, "there is at least one dragon with red eyes on this island!" and suddenly vanishes. the dragons freak out as eye colors are not supposed to be discussed on the island, but eventually they settle down upon seeing many other dragons with red eyes. 99 days later, 99 dragons are dead at noon. why?

The logician didn't tell them anything they weren't already aware of.If the dragons died, it wasn't because of that, it was some unrelated dragon catastrophe.

you got an answer or what?

The answer is that you framed the riddle totally wrong.Here it is in its correct glory:

The Problem

Three dragons are living on an island. On this island, dragons either have red eyes or blue eyes. If a dragon with red eyes realizes that he has red eyes, then he will die at midnight that night. There are no reflective surfaces on the island (i.e. there is no way for a dragon to see his own eye-colour). The three dragons never speak or communicate to each other in any way, but they do see each other everyday. Thus each dragon knows the eye-colour of the other two dragons. It turns out that all three dragons on this island have red eyes.

Many years pass without a dragon dying, because no dragon ever finds out his own eye-colour. One day, a cackling wizard appears in front of all three dragons and makes the statement, "At least one of you has red eyes!", and then disappears. The dragons know that the wizard never lies.

On the n-th night since the wizard appeared, all three dragons died. What is n, and how did the dragons realize that they had red eyes?

And the answer:

Spoiler

The Solution

I could give the solution for three dragons only, by breaking the situation down into four cases and handling each case; but I will do it a better, more elegant way. I will generalize this to any number of dragons, some with red eyes and some with blue.

Let the island have n > 0 dragons with red eyes, and m dragons with blue eyes. I claim that all n dragons with red eyes will die on the n-th night after the wizard makes the statement "At least one of you has red eyes." (So for the original problem, the answer is the 3rd night). I prove this using mathematical induction on n.

If n = 1, then the lone dragon with red eyes will look around the island and see that all other dragons have blue eyes. He concludes that he is the only one with red eyes, and thus dies on the first night.

Suppose that for n = k-1, k > 1, that all k-1 red-eyed dragons die on the (k-1)-th night. Then for n = k, this is what happens: each of the k dragons will look around and see that there are k-1 dragons with red eyes on the island. Each dragon thinks, "I don't want to die, so let's assume that I have blue eyes." Then each dragon should expect the other k-1 dragons to die in the (k-1)-th night; so they wait. On the k-th day, each dragon sees that the other k-1 dragons are still alive, and thus their initial assumption that "I have blue eyes" must be false. Thus each of the k dragons realize that they have red eyes, and die on the k-th night.

Either I'm stuipider than I thought, or this still doesn't make any sense.Clarification.....these two options are not mutually exclusive.

 

[(HULK)]

There is a common English word that is nine letters long. Each time you remove a letter from it, it still remains an English word - from nine letters right down to a single letter. What is the original word, and what are the words that it becomes after removing one letter at a time?

 

[(HULK)]

How can 4 be half of 5?