I need to do a project for Math with the subject: Antikythera mechanism. I was wondering if you could help me/ know a person who could help me with this project. The information on the internet isn't kind of enough for my research. I've watched many video's of you and thought maybe you could help me with my project. You're very inspiring and you make math fun btw :)
Igor knows that his spot must be white. If it were black then both of the other two would have seen one white spot and one black. They both know that there are only two black spots in total (from five) so that means that if one of them had a black spot then one of the other two would be able to see two black spots and therefore claim his spot to be white. Since neither make this claim Igor knows that the other two must be seeing a white spot on his back (and on the other).
@minkusbc this problem doesn't work, because in the end logically you end up with two possibilities: qwerty saw 1 black, 1 white, uiop saw 1 black, 1 white. In this case Igor could be black and both qwerty and uiop would have no way of knowing what they were wearing. Similarly Qwerty and Uiop could have both seen white, and again wouldn't be sure what was on their own backs, therefore IGOR can't make an assumption.
@TasteForDisaster Yes, but we are 'given' that Igor sees two white spots. If he (or any of them) saw one white spot and one black, then (as you imply), the same logic applies. Perhaps the puzzle would be better if we are given the spots on all three prisoners as: 1(W), 2(W), 3(B); we then have to work out which of them correctly asserts his spot colour, and how he knew this. Regards.
It can be easily solved saying IGOR must have black because if he has white they would stuck forever since they all have the same colour. then all have the same position.
Igor has a black spot on his back. Since he sees the two white spots on the other men he concludes his must be black because the other two men see one black and one white and are not certain that they can come to a definite answer as to which color was on his own back. The other two men were unsure, therefore could not arrive at an answer.
Since we are preposing the idea that they are all as smart as me.
1) If i saw two blacks, then i am automatically white.
2a) If i saw one black and one white, i am white or black;
2b) If i were black then one of the other members woudl've spoken up by now, unless they are dumber than me. So i would have to be white.
3) If we all had white and all as intelligent as me (Your ave Americano), then we'd be all sitting here fiddling our thumbs for atleast 7min. The time it took me to deduce this.
I'm surprised that no one else picked up on the logical fallacy embedded within one of the suppositions. There actually is no way to deduce the answer from the information given. Anyone who has taken an advanced course in logic can tell you that the argument made in the solution to the answer is not valid, i.e. the form of the argument is such that true premises don't GUARANTEE a true conclusion. It makes no difference whether or not the premises are in fact true. The form is invalid........
I got the right answer, but not for the right reason (but yes, it was using logic). The thing is, I now understand it (some people don't even with the explanation)...
Now, we've figured out that all three prisoners have a white disc, and we've proven that a prisoner should be able to figure out he has a white disc upon seeing two other white discs.
If Qwerty is truly as smart as Igor, he would know that if both Igor and Uiop both had a white disc, he too would have a white disc and would have left already. Since he hasn't said anything, Igor knows he does not have a white disc and must therefore have a black disc.
@Haelstrome Aha. Now you're thinking. But if you think your logic is more sound than Igor's, answer me this: Suppose are all wearing white discs. You and Qwerty use your argument and conclude that you are wearing black discs. Igor uses his solution, and concludes he's wearing a white disc. Which one is more intelligent?
@philnoll No, see, the question says that they are of similar intelligence. The solution is that all three have white (sorry for the spoiler). The solution says that logically if you see two whites, you should be able to conclude you have a white as well. If Igor used this logic (he has similar intelligence as me), he would leave at the same time you do. If he leaves any later, it can be assumed he has less intelligence. If he has less, how can you trust his logic to make your own conclusion?
@Haelstrome Yeah, I can see your point. The wording is problematic. We could rework it so that everyone gets a chance to leave the room when the lights go out. If we're all still here when the lights come back on, then we can all deduce our own color.
This can ultimately lead to an infinite loop of logic, based upon nothing more than assumptions. If we then assume that perhaps Qwerty is not quite as smart as Igor and perhaps would not know that he has a white disc, then who's to say he would realize what disc he had if he saw one black and one white?
Thus, we must conclude that you cannot be certain that they would realize what colour they have if given the opportunity because no matter the scenario, Qwerty and Uiop should have already left.
Igor sees that both his companions have white (there were 3 white disks in the bag, 2 black). So he would assum since NOW that there are more black then white disks (his companions having the 2 whites, which leaves only one white and 2 blacks) that he would have a black disk because there are more blacks now. The other two would have been nervous to try and guess because they see Igor's black and the other person's white and they wouldve been afraid to guess it wrong.
This is a parallel processing puzzle. Each prisoner is thinking the same as each other at the same time. The puzzle requires a jailor to ask them if they know their disk colour to bring logical order to the puzzle. If W W B there will be 1 'unknown' reply at which point each W disk prisoner knows they have a W disk. The B prisoner then knows he has a B disk and is too late to declare. If W W W then there will be 2 'unknown' replies at which point each prisoner knows they have a W disk.
i couldnt find the answer but i thought the answer was white and while thinking of my logic i thought the answer could of been black but i was constantly thinking that the countryleader didnt even ask a question so how could he do all that without guessing.. but then that had no part of my mission?? whats the answer anyone?
Igor sees white white. He concludes he has white. Qwerty sees white white also. Why couldn't he have reached the same conclusion? Or uiop, who also saw white white?
I think people are getting hung up on my phrase "they had equal intelligence". That does not mean that they are EXACTLY equal, they are "of similar" intelligence. However, even if their IQ's were all the same, it is possible for one of them to get a problem that the others do not, (at least right away).
Nice puzzle. This is like the Friday riddles my 6th grade teacher gave us. Very tricky if you overhtink it, but if you just relax you can get it. Here, ill send you one in a message on youtube.
4) Suppose Qwerty thinks if I had white and Igor saw it and he knew Uiop was white he would have figured out that he is white and gone so I must be black but then again if i was black and igor saw it he would have won knowing uiop is still here.So this again leaves a perfect doubt.
the stewardess used empathy not logic.reply please.
I wonder how the fictional Sherlock Holmes would have done on this. He had great deductive logic, but his observant eye was really the key to 90% of the solutions he came up with. I always admired people who can observe, because I sure as heck can't. Thankfully observation isn't really necessary in this problem. I sure didn't get it right away though.
Well, I guess it makes no sense to post the answer, since anyone can look it up at any time. Not going to impress anybody either way. All I'm going to say is Igor's in a good position. Only he knows what's left in the bag. Not easy to figure out. I kept thinking the idea was to try to figure the motivations of the others.
I just looked at the answer. That was too much crud to think about at once. I can't interpret the intentions of others.
For some reason I thought what Igor saw gave him enough information to conclude that there weren't two white disks still in the bag, and if there weren't two white disks, then he must have a black disk on his back.
It's easy, it's based on this, there cannot be two blacks amongst the prisoner, even if we do not know that that Igor saw two whites, because instantaneously, the one who saw two blacks will deduce he is white.
similarly, if either qwerty uiop sees black and white, they will instantaneously deduce that theirs is white, because the double black condition would have given them away.
The only reason why everyone was silent was because everyone was white, i.e. Igor was white
@garahehe Well he can guess even before the discs are drawn really. The test is supposed to be FAIR FOR ALL 3 PRISONERS. He may think: "if 2 of us wear black, the 3rd one will immediately guess he wears white (not fair). If only one of us wears black he will be in evident disadvantage, cause at seeing 2 whites he can't conclude nothing before his mates (as the video solution clearly explains). Therefore it would only be fair if we all wear white". This way he can win even before the test begins.
if you see two black discs you have a white and you would automatically leave.
if you see one white and one black and no one has left that means that no one is sure of what color they have, and you must have a white disc.
if you see no black discs and no one has left, and you believe that someone would have left using the previous logic because you are all of equal intelligence then you would leave and you would have a white disc on your back.
I'm not sure of the logic of your step 2. If I saw a black and a white disk, then I would think, "If I have a black disk, then the "White disk" guy would see two blacks and he would have left." But, he hasn't left, so I can't have a black, I must have a white. Then I agree with your statements 1 and 3 logic.
the whole thing behind the logic is that the 3 guys are all smart, and how much time passes while they are in there , if they are all in there and 1 guy sees a white and black and no one leaves that means no one is sure of what they have but that also means that the guy that sees white and black has a white, and then if no one leaves and no one left by the second logic then you leave using the the second logic and you must have a white thats all think about it ... it makes sense
thank you! this puzzle has been driving me crazy for ages!!! :D
monkeyboyzinaction 1 month ago
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it's not that great
zeth2885 1 year ago
Dear minkusbc,
I need to do a project for Math with the subject: Antikythera mechanism. I was wondering if you could help me/ know a person who could help me with this project. The information on the internet isn't kind of enough for my research. I've watched many video's of you and thought maybe you could help me with my project. You're very inspiring and you make math fun btw :)
iiCandyx 1 year ago
Igor knows that his spot must be white. If it were black then both of the other two would have seen one white spot and one black. They both know that there are only two black spots in total (from five) so that means that if one of them had a black spot then one of the other two would be able to see two black spots and therefore claim his spot to be white. Since neither make this claim Igor knows that the other two must be seeing a white spot on his back (and on the other).
7x34hj 1 year ago
@7x34hj You nailed it! Superb logic.
minkusbc 1 year ago
@minkusbc Much gratitude, sir.
7x34hj 1 year ago
@minkusbc this problem doesn't work, because in the end logically you end up with two possibilities: qwerty saw 1 black, 1 white, uiop saw 1 black, 1 white. In this case Igor could be black and both qwerty and uiop would have no way of knowing what they were wearing. Similarly Qwerty and Uiop could have both seen white, and again wouldn't be sure what was on their own backs, therefore IGOR can't make an assumption.
gravi1ty 1 month ago
@7x34hj but he see's 2 white marks. it would work like you said if igor saw a white and black disk.
TasteForDisaster 8 months ago
@TasteForDisaster Yes, but we are 'given' that Igor sees two white spots. If he (or any of them) saw one white spot and one black, then (as you imply), the same logic applies. Perhaps the puzzle would be better if we are given the spots on all three prisoners as: 1(W), 2(W), 3(B); we then have to work out which of them correctly asserts his spot colour, and how he knew this. Regards.
7x34hj 8 months ago
nah, you're wrong, try again.
gravi1ty 1 month ago
It can be easily solved saying IGOR must have black because if he has white they would stuck forever since they all have the same colour. then all have the same position.
Since IGOR got out, so he must be different.
Xmuslim2010 1 year ago
no offence but you have to be really poor in logic to not figure it out in like 2 min without hints ...
alfaxen1 1 year ago
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philnoll 1 year ago
@alfaxen1 Great for you! But what is the answer and what is your logic?
minkusbc 1 year ago
@minkusbc has been answerd so many times its no use in me writing it 2.. it be like spaming xD
alfaxen1 1 year ago
Igor has a black spot on his back. Since he sees the two white spots on the other men he concludes his must be black because the other two men see one black and one white and are not certain that they can come to a definite answer as to which color was on his own back. The other two men were unsure, therefore could not arrive at an answer.
Andrew Stephens Greenville SC
andrewmstephensIII 1 year ago
Since we are preposing the idea that they are all as smart as me.
1) If i saw two blacks, then i am automatically white.
2a) If i saw one black and one white, i am white or black;
2b) If i were black then one of the other members woudl've spoken up by now, unless they are dumber than me. So i would have to be white.
3) If we all had white and all as intelligent as me (Your ave Americano), then we'd be all sitting here fiddling our thumbs for atleast 7min. The time it took me to deduce this.
D4R3W 1 year ago
im guessing he has white on his back so that all three prisoners would have the same problem to solve
sitepath 1 year ago
I'm surprised that no one else picked up on the logical fallacy embedded within one of the suppositions. There actually is no way to deduce the answer from the information given. Anyone who has taken an advanced course in logic can tell you that the argument made in the solution to the answer is not valid, i.e. the form of the argument is such that true premises don't GUARANTEE a true conclusion. It makes no difference whether or not the premises are in fact true. The form is invalid........
brianallenmetzger 1 year ago
ahhhhhhhh Igor!!!!!
bigbrownfrank 1 year ago
I got the right answer, but not for the right reason (but yes, it was using logic). The thing is, I now understand it (some people don't even with the explanation)...
This definitely is a great puzzle.
Xclann 1 year ago
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Now, we've figured out that all three prisoners have a white disc, and we've proven that a prisoner should be able to figure out he has a white disc upon seeing two other white discs.
If Qwerty is truly as smart as Igor, he would know that if both Igor and Uiop both had a white disc, he too would have a white disc and would have left already. Since he hasn't said anything, Igor knows he does not have a white disc and must therefore have a black disc.
Haelstrome 1 year ago
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Haelstrome 1 year ago
@Haelstrome Aha. Now you're thinking. But if you think your logic is more sound than Igor's, answer me this: Suppose are all wearing white discs. You and Qwerty use your argument and conclude that you are wearing black discs. Igor uses his solution, and concludes he's wearing a white disc. Which one is more intelligent?
philnoll 1 year ago
@philnoll The hint should really say "average intelligence," not "equal intelligence"
philnoll 1 year ago
@philnoll No, see, the question says that they are of similar intelligence. The solution is that all three have white (sorry for the spoiler). The solution says that logically if you see two whites, you should be able to conclude you have a white as well. If Igor used this logic (he has similar intelligence as me), he would leave at the same time you do. If he leaves any later, it can be assumed he has less intelligence. If he has less, how can you trust his logic to make your own conclusion?
Haelstrome 1 year ago
@Haelstrome Yeah, I can see your point. The wording is problematic. We could rework it so that everyone gets a chance to leave the room when the lights go out. If we're all still here when the lights come back on, then we can all deduce our own color.
philnoll 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
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Haelstrome 1 year ago
This can ultimately lead to an infinite loop of logic, based upon nothing more than assumptions. If we then assume that perhaps Qwerty is not quite as smart as Igor and perhaps would not know that he has a white disc, then who's to say he would realize what disc he had if he saw one black and one white?
Thus, we must conclude that you cannot be certain that they would realize what colour they have if given the opportunity because no matter the scenario, Qwerty and Uiop should have already left.
Haelstrome 1 year ago
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Haelstrome 1 year ago
Igor would have felt better at guessing then his two companions. I don't know if this is right, I'm gonna go see.
commenterofsorts 1 year ago
Igor sees that both his companions have white (there were 3 white disks in the bag, 2 black). So he would assum since NOW that there are more black then white disks (his companions having the 2 whites, which leaves only one white and 2 blacks) that he would have a black disk because there are more blacks now. The other two would have been nervous to try and guess because they see Igor's black and the other person's white and they wouldve been afraid to guess it wrong.
commenterofsorts 1 year ago
In case of confusion the 'unknown' replies are made collectively, not by an individual prisoner.
justaviewer123 1 year ago
This is a parallel processing puzzle. Each prisoner is thinking the same as each other at the same time. The puzzle requires a jailor to ask them if they know their disk colour to bring logical order to the puzzle. If W W B there will be 1 'unknown' reply at which point each W disk prisoner knows they have a W disk. The B prisoner then knows he has a B disk and is too late to declare. If W W W then there will be 2 'unknown' replies at which point each prisoner knows they have a W disk.
justaviewer123 1 year ago
opps sorry about the bad rating i did not mean to click on the rating so sorry :)
RazerSkater101 2 years ago
*~*~*~* SPOILER ANSWER *~*~*~*
Putting yourself in the person's position, if Igor had 1 black disk and your other friend had 1 black disk, you would have left long ago.
DarigonKogi 2 years ago
and everyone is arguing over equal intelligence as being so important in the question..?? wtf really?
poopz 2 years ago
i couldnt find the answer but i thought the answer was white and while thinking of my logic i thought the answer could of been black but i was constantly thinking that the countryleader didnt even ask a question so how could he do all that without guessing.. but then that had no part of my mission?? whats the answer anyone?
poopz 2 years ago
i cant get the answere when i click on the link a bunch of encoding comes up on word
MagicGuy2009 2 years ago
wow, cool puzzle, ugh i have to admit i had to look at the answer lol =/
4seer 2 years ago
So easy... Got it right away.
neonmix89 2 years ago
Igor sees white white. He concludes he has white. Qwerty sees white white also. Why couldn't he have reached the same conclusion? Or uiop, who also saw white white?
ericsosna 2 years ago
I think people are getting hung up on my phrase "they had equal intelligence". That does not mean that they are EXACTLY equal, they are "of similar" intelligence. However, even if their IQ's were all the same, it is possible for one of them to get a problem that the others do not, (at least right away).
minkusbc 2 years ago
Nice puzzle. This is like the Friday riddles my 6th grade teacher gave us. Very tricky if you overhtink it, but if you just relax you can get it. Here, ill send you one in a message on youtube.
conquestvideos 2 years ago
@minkusbc
1)Cannot apply in real life
2)Igor was more intelligent
3)Even if they were equal ,they didn't know that
4) Suppose Qwerty thinks if I had white and Igor saw it and he knew Uiop was white he would have figured out that he is white and gone so I must be black but then again if i was black and igor saw it he would have won knowing uiop is still here.So this again leaves a perfect doubt.
the stewardess used empathy not logic.reply please.
kiranrajkeralaboy 6 months ago
I know a similar problem. We worked on it with my friend when we were math student. And I found it right away. They couldn't believe it!
I'll put my problem as a response to yours when I release it.
TyYann 2 years ago
I wonder how the fictional Sherlock Holmes would have done on this. He had great deductive logic, but his observant eye was really the key to 90% of the solutions he came up with. I always admired people who can observe, because I sure as heck can't. Thankfully observation isn't really necessary in this problem. I sure didn't get it right away though.
theboombody 2 years ago
Well, I guess it makes no sense to post the answer, since anyone can look it up at any time. Not going to impress anybody either way. All I'm going to say is Igor's in a good position. Only he knows what's left in the bag. Not easy to figure out. I kept thinking the idea was to try to figure the motivations of the others.
theboombody 2 years ago
Oh shoot, I think I got the answer wrong. Oh well. It's late, so I'm not going to worry about it.
theboombody 2 years ago
No, Igor does not know what is left in the bag, none of the prisoners were shown what was left in the bag.
minkusbc 2 years ago
I just looked at the answer. That was too much crud to think about at once. I can't interpret the intentions of others.
For some reason I thought what Igor saw gave him enough information to conclude that there weren't two white disks still in the bag, and if there weren't two white disks, then he must have a black disk on his back.
theboombody 2 years ago
lmao took me like 10 secs the 2 hints gave it away tbh
ashfia76 2 years ago
I know a other puzzle, it looks something like this one not a 100%. But the answer was just the same :)
ExtremeProPower 2 years ago
It's easy, it's based on this, there cannot be two blacks amongst the prisoner, even if we do not know that that Igor saw two whites, because instantaneously, the one who saw two blacks will deduce he is white.
similarly, if either qwerty uiop sees black and white, they will instantaneously deduce that theirs is white, because the double black condition would have given them away.
The only reason why everyone was silent was because everyone was white, i.e. Igor was white
arthritismutilans 2 years ago
so whats teh answer??
poopz 2 years ago
Black
alanrolflol 2 years ago
@poopz
all three are white
the fun part is figuring out why ;)
exce11er 2 years ago
great puzzle!
although there is a second and much darker solution to this puzzle that is not very well known
scotland7yard 2 years ago 4
@scotland7yard whta is it? come on dont leave us hanging
garahehe 1 year ago
@garahehe Well he can guess even before the discs are drawn really. The test is supposed to be FAIR FOR ALL 3 PRISONERS. He may think: "if 2 of us wear black, the 3rd one will immediately guess he wears white (not fair). If only one of us wears black he will be in evident disadvantage, cause at seeing 2 whites he can't conclude nothing before his mates (as the video solution clearly explains). Therefore it would only be fair if we all wear white". This way he can win even before the test begins.
scotland7yard 1 year ago
if you see two black discs you have a white and you would automatically leave.
if you see one white and one black and no one has left that means that no one is sure of what color they have, and you must have a white disc.
if you see no black discs and no one has left, and you believe that someone would have left using the previous logic because you are all of equal intelligence then you would leave and you would have a white disc on your back.
macdaddy998 2 years ago
I'm not sure of the logic of your step 2. If I saw a black and a white disk, then I would think, "If I have a black disk, then the "White disk" guy would see two blacks and he would have left." But, he hasn't left, so I can't have a black, I must have a white. Then I agree with your statements 1 and 3 logic.
minkusbc 2 years ago
the whole thing behind the logic is that the 3 guys are all smart, and how much time passes while they are in there , if they are all in there and 1 guy sees a white and black and no one leaves that means no one is sure of what they have but that also means that the guy that sees white and black has a white, and then if no one leaves and no one left by the second logic then you leave using the the second logic and you must have a white thats all think about it ... it makes sense
macdaddy998 2 years ago
that wasn't too hard. maybe I was just lucky to think on the right tracks straight away.
for the record I'm fairly bad at maths. which is why i subscribe to you :)
Blenkey117 2 years ago
My brain exploded thinking about this. In the end I was still unsure of my answer so I couldn't resist checking online.
Great puzzle though.
wraith7396 2 years ago
you could have just posted the link on the side next to the description to make it easier, cool website and great brain teaser.
Chitownboy1023 2 years ago
it took me 40 mins omg nice nice nice :)
MELIPAISITA 2 years ago