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Topic: Pop Quiz Riddle (Read 78934 times) |
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Jackass
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anyone know the answer to the pop quiz riddle? ??
Because I don't. 
//Question moved from title, title changed by Icarus
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| « Last Edit: Sep 1st, 2003, 7:26pm by Icarus » |
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pio
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Re: anyone know the answer to the pop quiz riddle?
« Reply #1 on: Jul 30th, 2002, 5:33am » |
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Well, I don't know if this is the right answer, but to me the students premise is false:
"It can't be in friday because then we would know it on thursday"
And? What's the problem with knowing it when there's none left? It can perfectly be on friday. They would find it out on thursday, ok. But that's not a premise to base the rest of the reasoning.
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #2 on: Jul 30th, 2002, 7:32am » |
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Because on friday it won't be a surprise test anymore, the professor said it would be a _surprise_ test. He can't hold it on friday since the students will not be surprised, rendering his premise it would be a surprise test false.
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Neil Sedaka
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Re: anyone know the answer to the pop quiz riddle?
« Reply #3 on: Jul 30th, 2002, 8:05am » |
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Which is why leaving it until Friday would be THE BIGGEST surprise possible!
Pity the students as they studied each night up to and including Wednesday night, each time increasingly sure that the test would be the next day.
The surprise actually hits them on Thursday!
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Gamer555
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Re: anyone know the answer to the pop quiz riddle?
« Reply #4 on: Jul 30th, 2002, 8:37am » |
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You two bring up an interesting paradox. If the teacher said "You won't be able to figure out when it is" meaning it will be a TOTAL surprise, the students logic would work. But if the test isn't gone until Thursday (the students are at home on wednesday night) they won't know when it is. It could be on thursday, or on friday.
Logic if the popquiz is a TOTAL surprise (meaning they will never know when it is, until they get the pop quiz)
If it is thursday night, the pop quiz must be on friday and it wouldn't be a surprise (because friday is the only day left)
If it was wednesday night, the pop quiz must be on thursday. If it was on friday, it wouldn't be a surprise (because friday was the only day left). Since it can only be on one day that would be a surprise at all, it would be known when it must be, and so it wouldn't be a surprise.
If it was tuesday night, the students could rule out friday, and thursday (because it wouldnt be a surprise as listed above) and so wednesday is the only day left to have the quiz. Since only one day can be had for the quiz, it isn't a surprise.
If it was monday night, the students could rule out friday, thursday, and wednesday. So Tuesday is the only day left, and it wouldn't be a surprise.
Similar logic can be used... see?
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #5 on: Jul 30th, 2002, 8:38am » |
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Still if thursday passed without test, the test is no _surprise test_ anymore, due to this he canot be held as such.
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Gamer555
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Re: anyone know the answer to the pop quiz riddle?
« Reply #6 on: Jul 30th, 2002, 9:00am » |
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Are you agreeing with me? 
If the teacher means "I am planning to give a test this week. If you know when it is, and you are right, I will cancel it." Then it can be on anyday but friday.
If it was wednesday night, they wouldn't know when it was. Here is what I mean:
The test has no problem with Friday. It won't happen, because the students can cancel it, but that still doesn't stop them from planning the test. If the teacher says "I *WILL* give a test this week" instead of "I am planning to" then it would be the same as "it *WILL* be a secret (See previous post)"
If it was wednesday night, they couldn't say if it was thursday or friday. If it was thursday, they couldn't rule out friday, because it can still be planned then, and since that makes *2* days not *1* day. I hope this makes sense!
Similar logic can be applied to the other days... see?
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #7 on: Jul 30th, 2002, 9:58am » |
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Yes, Well I replied to the post before yours, yours got in between, and well I agree with that.
The problem here is that this riddle here is a bit modified, invalidly IMHO, disquising the orignal paradox. In this case the students suppose the teacher is mean, and don't want them to get away with a test, however that is not a must be. They can't say if the professor wants them to guess the day friday right.
The orignial problem is formulated simpler, not opening this loop hole. The professor just tells the students there will be a surprise examination next week. [suprise in the meaning it will be a surprise the moment he deals out the papers.]. One stutend goes to him and explains the reasoning above. There just can't be a surprise examination on Friday, it wouldn't be a surprise then. So Friday is ruled, so on Thursday also can't be a surprise examination, since it wouldn't be a surprise, and so on.
Now what's wrong with logic?
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Alex
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Re: anyone know the answer to the pop quiz riddle?
« Reply #8 on: Jul 30th, 2002, 2:18pm » |
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Take, for example, that it is Tuesday night. You declare that it cannot be on Friday because that wouldn't be a surprise as of Thursday night. Since it cannot be on Friday, then on Wednesday night it would be obvious that it is on Thursday, because Friday would be obvious. Therefore, since having the test on Thursday would be too obvious, it must be on Wednesday, right?
Prediction is assumed in this scenario. You are assuming that the teacher will decide to give the quiz on the most unpredictable day, when the riddle says nothing of this. The quiz will simply be on a random day. It might be Friday. It might be Monday.
I truly have no idea how to solve this riddle.
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Nicodemus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #9 on: Jul 30th, 2002, 3:03pm » |
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Let me contribute my thoughts on this problem. I think it's a correct solution, but unlike problems with numerical answers, it's difficult to empirically determine when an answer is "correct".
First, as I read the problem, the teacher announces that there will be a surprise quiz. The meaning of this is "on a given night, the students cannot deduce whether or not there will be a quiz the following day". If they can deduce the day the quiz was planned for, then the quiz will be cancelled. Note that the planning of a quiz and the actual quiz taking place are not the same thing; it can be planned for a day but then cancelled because the students were able to deduce the day correctly.
The tricky part of the problem is that it attempts to create logical propositions without attaching required context. Specifically, the logical propositions are valid only at certain times. Let's restate the first line of the problem logic with this implicit assumption spelled out:
1) If the quiz didn't happen on Thursday and it's Thursday evening, then the quiz is on Friday.
We cannot know before Thursday evening that the quiz did not occur on Thursday. We are not told that the quiz isn't Thursday, so the only way we can find out is to wait for Thursday to pass. Once we reach Thursday evening with no quiz, then we can deduce that the quiz is on Friday.
Now, if we revisit the problem, the rest of the logic is moot. It all relies on the assumption that it can't be Friday since we'd be able to deduce that it is Friday. However, this proposition only becomes true once it is Thursday evening. At any time before, we cannot satisfy the prerequisites of proposition 1.
Thus, at any time before the end of class on Thursday, the quiz can be any day. Thus the quiz can be on Tuesday without violating any rules.
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Gamer555
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Re: anyone know the answer to the pop quiz riddle?
« Reply #10 on: Jul 30th, 2002, 8:28pm » |
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Yes, what Nicodemus said above is what happens when the teacher doesn't make it SURPRISE all the way. So, it is a good explanation of the problem! Good job...
SURPRISE all the way means the students will never know when the test is, until it is handed out.
Alex, nobody ever said it the teacher favored over days, simply he can't choose from days that aren't a SURPRISE all the way If the quiz is SURPRISE all the way (like the kids thought) then it can't be any day.
Logic if the popquiz is a TOTAL surprise (meaning they will never know when it is, until they get the pop quiz)
If it is thursday night, the pop quiz must be on friday and it wouldn't be a surprise (because friday is the only day left)
If it was wednesday night, the pop quiz must be on thursday. If it was on friday, it wouldn't be a surprise (because friday was the only day left). Since it can only be on one day that would be a surprise at all, it would be known when it must be, and so it wouldn't be a surprise.
If it was tuesday night, the students could rule out friday, and thursday (because it wouldnt be a surprise as listed above) and so wednesday is the only day left to have the quiz. Since only one day can be had for the quiz, it isn't a surprise.
If it was monday night, the students could rule out friday, thursday, and wednesday. So Tuesday is the only day left, and it wouldn't be a surprise.
(If it was sunday night, Monday would be the only day left, other than tuesday, wednesday, thursday, and friday)
Note that if his meaning of a "surprise quiz" is a "SURPRISE all the way quiz" then he lied. But if it isn't, he didn't... To summarize Nicodemus' ideas:
You can't rule something out that hasn't happened yet, if you can't be sure it is happening.
Also, my other idea from one of my first posts:
The test has no problem with Friday. It won't happen, because the students can cancel it, but that still doesn't stop them from planning the test. If the teacher says "I *WILL* give a test this week" instead of "I am planning to" then it would be the same as "it *WILL* be a secret (See previous post)"
If it was wednesday night, they couldn't say if it was thursday or friday. If it was thursday, they couldn't rule out friday, because it can still be planned then, and since that makes *2* days not *1* day. I hope this makes sense!
Do you understand?
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Nicodemus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #11 on: Jul 30th, 2002, 9:50pm » |
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Gamer, I think I see the distinction you're talking about. Let me see if I can restate it:
We can use a stricter definition of surprise meaning that the students won't know when the test is, even the night before. This slight difference in meaning has major implications: If the professor is limited to picking a day that will be a strict surprise, then he cannot choose Friday because at some time before Friday it becomes predictable. Specifically, Thursday evening it becomes obvious the test is Friday.
Thus we eliminate Friday completely. Our strict definition removes the temporal prerequisite from the proposition by disallowing days that will ever become predictable.
My other argument hinged on the ability to discard the unconditional conclusion "it can't be Friday". Under the strict surprise definition, this is now a valid conclusion. Therefore we can follow the logical chain of the reasoning put forth by the students... Each successive day uses the same logical argument as the available days in the week diminish. Eventually, there are no days remaining, so there cannot be a test.
Gamer, I hope I summarized your argument correctly?
If so, we can at last explain the problem (in mind-numbing detail). The flaw in the students' reasoning (since evidently there was a quiz) was in their interpretation of the word "surprise". They followed the above chain of logic from that premise, while the professor followed the logic I and others detailed before.
Now Mr. Wu can remove the "unsolved" mark on this problem! 
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #12 on: Jul 30th, 2002, 10:44pm » |
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No he can't. Who said the professor followed your or the others logic? He can as well follow the students logic, saying the quiz will be a surprise on the day it's handed out. It was a surprise just then, wasn't it?
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Nicodemus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #13 on: Jul 31st, 2002, 12:10am » |
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Quote:| He can as well follow the students logic, saying the quiz will be a surprise on the day it's handed out. It was a surprise just then, wasn't it? |
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That sounds like the solution we arrived at. If he was following the student's logic, there cannot be a quiz because it is a logical contradiction (between there being a quiz and it being a surprise). If he does give a quiz anyway (as you say and as stated in the problem), then it must be because he is using a different interpretation of "surprise" in his original statement, as explained above. (Or he flat out lied, but we're overlooking that.)
So where does your example disagree with this solution?
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #14 on: Jul 31st, 2002, 1:03am » |
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I refrain from putting this thing back to shelf too fast, we may be on the right track, but doesn't mean we solved it.
"then it must be because he is using a different interpretation of "surprise" in his original statement, as explained above. (Or he flat out lied, but we're overlooking that.) "
So thats okay let's look on the professor. Can we really overlook that he flat out lied? Maybe he just did.
I think a key on understanding the true problem is to modify the number of dates the professor anounces that a surprise test will be possible. Let's call it n. So in the original puzzle n is 5. I think the size of n doesn't actually matter to the problem. Now what happens if n would be 2, there is a suprise test tomorrow or the day after tomorrow. Or let's go even more extreme, let's make n 1. "The will be a surprise test tomorrow." Huh? His argument is just invalid, false. However the students consider is argument to be false, and are surprised by the test, so the argument was actually valid in this case.
So I think this neares the core of the problem. Okay you're solution is bailing out of this paradox, since you suppose the professor wanted to say a valid argument, and was only interpreted false, or just mismatched words a bit. You suppose he didn't want to lie or tell a paradox. But suppose he just did. His argument became valid after he dealt out the test, so he didn't lie at the end.
I think we must go a bit out of the box, and think further about the vality of the professors statement, and how it changes out of the circumstances. Initally the statement on the week before is inlogic, or invalid. But then the students realized it as such, and it became valid then.
Can you say that vality does change of time? Does vality change from the sight of the observer?
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Gamer555
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Re: anyone know the answer to the pop quiz riddle?
« Reply #15 on: Jul 31st, 2002, 5:20am » |
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I don't quite understand what you said before... Can somebody smarter explain it to me?
on Jul 31st, 2002, 1:03am, anshil wrote: His argument became valid after he dealt out the test, so he didn't lie at the end.
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The question I am having is: What does surprise mean? Does it mean surpise-all-the-way, or just "I won't tell you when the test is"? If it is surprise-all-the-way, he still lied... If it the other interpretation, the students were wrong.
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #16 on: Jul 31st, 2002, 6:52am » |
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It's surprise all the way, or otherwise he said something different as he ment, and we suppose that he said the thing he ment.
In the end his invalid statement is valid, since the students considered it to be invalid and didn't expect a test, so they got a surprise test in the next week as it was proclaimed.
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icon
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Re: anyone know the answer to the pop quiz riddle?
« Reply #17 on: Jul 31st, 2002, 9:17am » |
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i wanted to give my thoughts on this issue:
i feel that this is the main problem here:
(am gonna comment my thoughts on each quote from the riddle which i think is easiest to follow)
The students get together and decide that the quiz can't be on Friday, as if the quiz doesn't happen by Thursday, it'll be obvious the quiz is on Friday
(perhaps this is true but its ONLY can be true at 1 point of time(area thursday afterschool/friday befor school, which makes it before then a total suprise(however following this kind of logica we can take out friday).
Similarly, the quiz can't be on Thursday, because we know it won't be on Friday,(this is a mistake because you cant know that it CANT be on friday until thursday night! therefore in quiz will be given on thursday it will be within rules and a surpise for student(since this is the flaw in thier logic) and if the quiz doesn't happen by Wednesday, it'll be obvious it's on Thursday [because it can't be on Friday)]
(this is same as statement above, you will not know if the quit be on thursday until thursday evening and not by wednesday evening since it can be thursday or friday(mind you friday exception only comes into play in thursday evening!)).
Same thing for Wednesday, Tuesday and Monday. So it can't be on ANY day, so there's no quiz next week!"
its an intresting problem but i dont see how you can predict the days when it will happen since its a even 20% chance to do so
chance becomes much higher as each given day goes by however you still cant really predict it
i think teacher 'confused' students by saying he will not give quit if they can predict, therefore giving students a false sense(that there is an answer if you look hard enough(logically) you can reach it) while there wasnt 1
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Gamer555
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Re: anyone know the answer to the pop quiz riddle?
« Reply #18 on: Jul 31st, 2002, 12:13pm » |
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on Jul 30th, 2002, 9:50pm, Nicodemus wrote:Gamer, I think I see the distinction you're talking about. Let me see if I can restate it:
We can use a stricter definition of surprise meaning that the students won't know when the test is, even the night before. This slight difference in meaning has major implications: If the professor is limited to picking a day that will be a strict surprise, then he cannot choose Friday because at some time before Friday it becomes predictable. Specifically, Thursday evening it becomes obvious the test is Friday.
Thus we eliminate Friday completely. Our strict definition removes the temporal prerequisite from the proposition by disallowing days that will ever become predictable.
My other argument hinged on the ability to discard the unconditional conclusion "it can't be Friday". Under the strict surprise definition, this is now a valid conclusion. Therefore we can follow the logical chain of the reasoning put forth by the students... Each successive day uses the same logical argument as the available days in the week diminish. Eventually, there are no days remaining, so there cannot be a test.
Gamer, I hope I summarized your argument correctly?
If so, we can at last explain the problem (in mind-numbing detail). The flaw in the students' reasoning (since evidently there was a quiz) was in their interpretation of the word "surprise". They followed the above chain of logic from that premise, while the professor followed the logic I and others detailed before.
Now Mr. Wu can remove the "unsolved" mark on this problem! |
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Yes, that is *Exactly* what I have been saying. Sorry I missed this before!
I also think what Icon was saying, "i think teacher 'confused' students by saying he will not give quit if they can predict, therefore giving students a false sense(that there is an answer if you look hard enough(logically) you can reach it) while there wasnt 1 " is true too.
Summary solution: The students thought the teacher meant "strict surprise" or "surprise-all-the-way" but the teacher really just meant "You won't know what day I am going to test you"
I am not saying the teacher's definition precludes him from giving the test any day.
I am also not saying he favors days at the end of the week (like Friday and Thursday) more than days at the beginning of the week (like Monday and Tuesday) when it is Saturday or Sunday.
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icon
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Re: anyone know the answer to the pop quiz riddle?
« Reply #19 on: Jul 31st, 2002, 12:27pm » |
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i think the question here is not how to predict what day teacher was to give quiz(since most people went this way to explain how it wont be a suprise on friday if by thursday its not given so it wont be given at all then) but what the flaw in students logic
flaw is: they tried to logically predict what day teacher will give the quiz, which cant be done unless you doing a guess
(all the logic about it cant be friday/etc is pure bolony since it doesnt work if he gives quit on monday then all the stuff about other days cant be quiz days wouldnt work)
this is a case of over thinking the problem hehe
perhaps william can comment
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Nicodemus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #20 on: Jul 31st, 2002, 12:32pm » |
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I tend to agree with your analysis, Icon.
Anshil, you raised the question:
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let's look on the professor. Can we really overlook that he flat out lied?
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An interesting point. I discarded this option because I think that the riddle has a tendancy to collapse without it. If the professor lies, then we have no proposition on which to base any logic, since we must discard his statements. The answer to where the flaw in the students' logic was becomes "believing him".
But then you went with the assumption, as far as I can see, that the professor didn't lie in the sense that his original prediction came true: there was a quiz and it was a surprise.
Yet we can arrive at this conclusion without assuming his statements are false in any way. This leads back to the multiple interpretations of "surprise"; his original statements appear false if you choose one meaning (total surprise) yet appear true if you choose the other (not predictable).
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In the end his invalid statement is valid, since the students considered it to be invalid and didn't expect a test, so they got a surprise test in the next week as it was proclaimed.
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If I read your argument correctly, then he meant strict surprise, just as the students used in their logic. If the test was ever predictable before the moment it was handed out, it would be cancelled. Since the students reasoned from this logic, it was predictable and cancelled.
Yet he didn't cancel it (and that's a surprise). The cancelled/not cancelled paradox is brought about by the fact that we started with a false premise; specifically, the professor lied when he said he'd cancel the quiz if it were predictable. The paradox is simply the result of reasoning from false premises -- a proof by contradiction.
There is no contradiction between his other statement that the quiz will be a surprise. It was. But that seems to me irrelevant, since we've demonstrated that the puzzle's premise itself was false for that interpretation of "surprise".
Hence, also given the assumption that riddles contain only true premises (otherwise we can break rules willy nilly and they aren't riddles!), we conclude that the professor was interpreting the meaning of "surprise" differently, which was our solution.
How does that measure up to your thinking? Convincing or did I miss something?
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anshil
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Re: anyone know the answer to the pop quiz riddle?
« Reply #21 on: Jul 31st, 2002, 1:03pm » |
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Well I ask you do you find your answer really satisfying?
In my understanding a suprise test is a suprise test, it actually can't be announced. That's something different than a test on an untold day. A suprise test can't be on a day where it's 100% sure it will come. I think it's not right to say well the professor interpreted his own words wrong and actually ment the on any day variant.
The professor didn't lie in the part when he told the students the test will be canceled if the guess the day correctly, did the students tell him on which day the test will be? No. However this test will be canceled when guessed rightly is an enhancement to the puzzle by I.M._Smarter_Enyu who posted it here. It's actually not necessary to the puzzle soI don't think it's important to the solution.
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Nicodemus
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Re: anyone know the answer to the pop quiz riddle?
« Reply #22 on: Jul 31st, 2002, 3:18pm » |
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Well I ask you, do you find your answer really satisfying?
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Yes, though I'm still open to further ideas. But this is the difficulty with such subjective problems; what one person might consider a sufficient explanation isn't convincing to someone else. (And that's just human nature, really.)
After reading your (great) comments in the other thread on this puzzle, I wanted to expound a bit more on some of my comments to clarify my position.
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In my understanding a suprise test is a suprise test, it actually can't be announced.
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This is quite an interesting point and gets right to the heart of the matter.
As I see it, the entire puzzle revolves around how we interpret the word "surprise". I would agree that your statement is correct for the strict interpretation of surprise; once we know that there will be a test, it can no longer be a total surprise. (If you remove the guessing of days, this is basically what the students attempted to prove.)
However, I put forth that you can still have a surprise test in a different sense; this is the loose interpretation of the word. The exact time of the test is a surprise, in that it's unpredictable, even though we know there will be a test sometime. I think that this is a valid reading of the professor's statements. (Heck, I even had a professor who gave announced-surprise tests like this!)
The entire problem hinges on this dual interpretation of the word "surprise". The apparent paradox in the puzzle comes from mixing these two different meanings in one context. The students consider it a strict surprise while the professor considers it a loose surprise.
Depending on how "surprise" is read, the problem changes. The students' logic is both fallacious and correct. The professor's proposition is both upheld and violated. Perhaps your comparison to quantum mechanics is quite apt?
Although this isn't a simple "solution" to the puzzle's question, I think that this answer serves to explain the puzzle itself. And that I consider a satisfactory resolution of the problem.
(Of course, it is always possible that this description is flawed. I'm not convinced --yet-- that it's inconsistent with any of the offered counterexamples, though.)
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The professor didn't lie in the part when he told the students the test will be canceled if they guess the day correctly, did the students tell him on which day the test will be? No.
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True. The students attempted to argue that any day would be impossible; their arguments only work for their strict interpretation of "surprise", though. From the professor's point of view, he has kept his word, as they haven't guessed the day. And if the professor is using the loose definition of "surprise", there is no way they can determine the day (prior to Thursday evening), other than blind guesswork.
Another reason that I think this explanation holds water is that we can quickly resolve the puzzle by forcing a single interpretation of "surprise". (Collapsing the quantum state, I guess the analogy would be.)
If we use the strict meaning of "surprise", then it must be true that the students cannot deduce the time of the quiz at any point before it is given, else it would be cancelled. This is consistent with the students' logic. Since the test happened regardless, the professor must have lied in saying he would cancel it (but not that it would be a surprise).
If we use the loose meaning of "surprise", then we can see the flaw in the students' reasoning. The time of the quiz cannot be deduced before Thursday, since there are two equally possible days. The professor's statements are consistent.
Forgive my long-windedness! I would like to concur with your conclusion that this problem is deceptively difficult.
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Re: anyone know the answer to the pop quiz riddle?
« Reply #23 on: Jul 31st, 2002, 3:33pm » |
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hehe
the most intresting part of this is basically the arguments both sides brought on definition of a supprise
i had a teacher back some years ago who i totally loved9as you can love any teacher in that sense of the word) as a person he was the person who actually was very funny and sometimes broke some rules but same time was pretty strict yet give u space if you justify it :>
and once in a while he should use some uses of physics in real world, which would associate with a 14 year old mind so he would go home and actually be intrested in that and not to go out and try to do all but think about the school work
reminds me once a poster he had about throwing a curve ball how the spin and the way you hold the ball makes it curve by creative a some sort of pressure so when it reaches it, it collapses and curves down(now mind you back then i was all sports and not lot of physics but this made me actually spend few days researching, where i found few other grips which would make the fall curve not from 12/6 but from 1/7 even 2/8(imagine clock)
what all this has to do with this ... well simple:> perhaps the proffesor knew that there is no way you can predict the quiz before thursday night(duh) with the information he gives
chances are this class had something to do with sciences so maybe his goal was to get people intrested in skipping the quiz and therefore do the research to skip(reverse psychology)
without realising so and therefore probably studing for the quiz itself
now i can be 100miles off course but i think this is intresting side point :>
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David Lischka
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Re: anyone know the answer to the pop quiz riddle?
« Reply #24 on: Jul 31st, 2002, 4:53pm » |
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Any old puzzle but a good un'
I believe that the Professor cannot actually fulfil his promise, in other words his constraints are mutually contradictory. Just like trying to divide 1 by 0 and get an integer answer.
I have never seen any better answer than this. But just in case there is an answer, let me recast the problem as a card game.
Dealer has 7 cards exactly one of which is the Jack of Spades. He lays the cards face down in a row in front of the player. The player turns the cards over, in order, one by one until he feels sure that the next card is the Jack (if he turns the Jack over by mistake the round ends there and then). He then bets whatever he likes that the card is a Jack and turns it over. If he's right then he collects from the dealer, if wrong then he pays the dealer. (The player pays a penny per round and if he turns the jack before he bets then he loses just his original penny)
Clearly the dealer has to surprise the player by placing the Jack otherwise he loses big time. So he can't afford to place the Jack in the 7th and final position in case the player turns over the first 6 and is then sure that the Jack is the 7th and final card. So far the puzzle is the same as the pop quiz.
But
Play the game many times. Would you rather be the dealer or the player?
Hint every time I play this I lose a lot at first and then end up winning $100, 000, 000 !!
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