View Full Version : A harder problem...one for GoT
aloiz
08-02-2004, 07:05 PM
Ran across this problem a couple of weeks ago, and found it quite challenging.
Question 1: What is the sum of all numerical answers in this quiz (including this one)?
Question 2: How many questions in this quiz have an answer of True?
Question 3: True or False - Question 1 has the highest numerical answer in this quiz.
Question 4: How many answers are the same as this one (including this one)?
Question 5: True or False - All numerical answers in this quiz are positive.
Question 6: What is the average of all numerical answers in this quiz (including this one)?
Question 7: True or False - The answer to question 4 is greater than the answer to question 2.
Question 8: What is the answer to question 1 divided by the answer to question 8?
Question 9: True or False - The answer to question 6 is equal to the difference between answers 2 and 4, minus the product of answers 8 and 4.
Question 10: What is the answer to this question?
aloiz
GuyOnTilt
08-02-2004, 07:08 PM
Man, now I'm going to have to go find a pencil...Can't believe I don't have one in my office. /images/graemlins/grin.gif
GoT
GuyOnTilt
08-02-2004, 07:21 PM
Question: Can Q10 have more than one answer??
GoT
aloiz
08-02-2004, 07:25 PM
I don't think I'll answer that just yet. If no one seems to be getting anywhere I'll throw out a few hints. However I will say as stated you should have enough information to answer the question without having to make any major assumptions.
aloiz
daryn
08-02-2004, 07:25 PM
#1 is impossible to answer
GuyOnTilt
08-02-2004, 07:26 PM
#1 is impossible to answer
No it's not. But #8 IS. This quiz is flawed. #8 has no solution.
GoT
jwvdcw
08-02-2004, 07:26 PM
I think every question is impossible...eating dinner now, will look at it again later.
aloiz
08-02-2004, 07:26 PM
Almost impossible but not quite. You're overlooking one case.
aloiz
daryn
08-02-2004, 07:28 PM
don't give me that infinity bull
aloiz
08-02-2004, 07:29 PM
No infinity is not an answer to any question.
aloiz
GuyOnTilt
08-02-2004, 07:31 PM
Okay, here's my answers assuming that Q10 can have 2 answers. HOWEVER, I think Q8 is flawed. But assuming I ignore that and pretend it's not, here's my answers:
<font color="white">1: 0
2: 2
3: False
4: 2
5: False
6: 0
7: False
8: 0*
9: True
10: True, -4
*The answer to #1 has to be zero or infinity, and for the sake of this quizlet, it's not going to be infinity. So #1 equals zero, and also has to be the square of #8, which states "What is the answer to question 1 divided by the answer to question 8?" This would mean that the answer to #8 also has to be zero, HOWEVER if #8 did equal zero, then that would mean the answer to #8 would be zero divided by zero, which has no solution. Therefore, the question is flawed.
I think...
Edit: I guess #1 could also be 1/infinity or -1/infinity... /images/graemlins/crazy.gif</font>
Edit: Just got a from the giver of the quiz saying my answer to Q1 is wrong, so I guess there goes that! Back to the drawing board!
GoT
daryn
08-02-2004, 07:34 PM
what is your logic? that the answer to 1 is infinity? i don't buy it.
aloiz
08-02-2004, 07:35 PM
Perhaps the wording of question one is a little confusing. A hint: answer to question 1 = answer to question 1 + sum(answers to all other numerical answers in quiz). Hope that makes things slightly more clear. In other words, Q1 does not have to be 0.
aloiz
GuyOnTilt
08-02-2004, 07:37 PM
hint: answer to question 1 = answer to question 1 + sum(answers to all other numerical answers in quiz).
That would make the answer to Q1 wrong though... It either has to be 0, inifinity, 1/infinity, or -1/infinity... If none of those are the answer, then could you reword the question correctly???
GoT
daryn
08-02-2004, 07:37 PM
yea number 1 must be zero, you're right.
The Armchair
08-02-2004, 07:37 PM
(Answers deleted) Nevermind. I screwed up.
daryn
08-02-2004, 07:39 PM
i'm with GOT here. as the question stands, the answer can't be a non-zero integer.
GuyOnTilt
08-02-2004, 07:41 PM
Your answers to 1 and 4 are definitely wrong, which just screws up the rest.
GoT
aloiz
08-02-2004, 07:42 PM
Alright if sum of answers to all other questions = 0 could the answer to Q1 be say 5 (5 = 5+0)? Although the question could be read as a re-occuring sequence it's not suppose to be.
aloiz
GuyOnTilt
08-02-2004, 07:43 PM
as the question stands, the answer can't be a non-zero integer.
Agreed. And since it can't be zero either, since that would make Q8 unanswerable, it has to be a non-integer solution as worded.
GoT
daryn
08-02-2004, 07:45 PM
</font><blockquote><font class="small">In risposta di:</font><hr />
Alright if sum of answers to all other questions = 0 could the answer to Q1 be say 5 (5 = 5+0)?
aloiz
[/ QUOTE ]
no.
GuyOnTilt
08-02-2004, 07:49 PM
Edit: Nevermind.
aloiz
08-02-2004, 07:49 PM
yes.
Not a reoccuring sequence. Let me rephrase the clarification. Answer to question 1 = Answer to question 1 + sum of all other numerical answers NOT INCLUDING QUESTION 1
Now does 5 = 5+0 satisfy that?
aloiz
daryn
08-02-2004, 07:54 PM
no.
daryn
08-02-2004, 07:55 PM
if the sum of all the other questions is 0, then the answer to #1 is zero, not 5.
jwvdcw
08-02-2004, 07:55 PM
[ QUOTE ]
yes.
Not a reoccuring sequence. Let me rephrase the clarification. Answer to question 1 = Answer to question 1 + sum of all other numerical answers NOT INCLUDING QUESTION 1
Now does 5 = 5+0 satisfy that?
aloiz
[/ QUOTE ]
well then why did you specifically type 'including this one' next to it??
aloiz
08-02-2004, 07:58 PM
That was supposed to make it clearer. If it had just been the sum off all numerical answers someone would have inevitably asked if that included the answer to question 1. It does.
aloiz
aloiz
08-02-2004, 08:03 PM
Yes 0 is a possiblity, and so is 1,2,3...
a = a + x
where a = answer to question 1
x = sum of answers to all other question not including question 1
Now let's do some basic algebra. Subtract 'a' from both sides and we get x = 0. So what can you conclude from q1?? All other numerical answers have to add up to 0.
aloiz
daryn
08-02-2004, 08:06 PM
i agree. also, a = 0.
GuyOnTilt
08-02-2004, 08:11 PM
No daryn, he's right.
Let's say the sums of all the other numerical questions besides Q1 add up to zero. Then we could make Q1 anything we wanted. It still could not be negative because of Q8, and I believe it would still have to be the largest numerical answer possible because of a combination of other questions, but it could be, say 36. 5 other numbers that add to zero plus 36 = 36. No need to repeat. It works. We both thought it had to be zero or infinity first because after we added it to itself, it woudl turn out to be something different and then it would be incorrect, but in this case it isn't; it's the same number and therefore an acceptable answer.
I still have issues with this quiz and think there is an error unless Q10 can have both a numberical answer and a T or F answer, in which case I have a solution for all answers.
Could you PM me your solutions aloiz so I can see if they get around the contradictions I'm finding? I'm done trying this quiz the way it's currently worded.
GoT
daryn
08-02-2004, 08:12 PM
so you're saying, just choose some arbitrary answer for #1? it's not that i didn't understand that, it's that i see that as bogus.
aloiz
08-02-2004, 08:13 PM
What about this equation a = a + x says that a = 0? It is possible that a = 0, but not necessary. The only thing necessary for that equation to be satisfied is that x = 0.
If you're really serious about what you're saying and not just dicking around, a little more depth into your line of reasoning would be nice. Replies like 'no', while amusing do not help me understand where you're coming from, as most likely this is just a semantics problem (although not if you agree with the equation above).
aloiz
aloiz
08-02-2004, 08:14 PM
Q1 cannot be determined without answering other questions first. The only thing question 1 tells you right off the bat is that the sum of all other answers must be 0. That should lead you to the answer of another question.
aloiz
GuyOnTilt
08-02-2004, 08:14 PM
so you're saying, just choose some arbitrary answer for #1?
Almost. At first it seems like it could be arbitrary, but it can't quite be. I believe it will have to be larger than any other answer, and also a perfect square. Which perfect square hinges on whether Q9 is true. If it is, then there is no perfect square that satisfies the quiz. If Q9 is false, then again I can't find a solution for the quiz without Q10 having both a T/F and numerical answer.
GoT
daryn
08-02-2004, 08:15 PM
it's not that i don't understand basic 7th grade algebra, it's just that what is a? if you are just picking some arbitrary number for a, i see it as a cop-out.
daryn
08-02-2004, 08:16 PM
i understand, but basically you are choosing what you want the answer to be.
aloiz
08-02-2004, 08:16 PM
[ QUOTE ]
If Q9 is false, then again I can't find a solution for the quiz with Q10 having both a T/F and numerical answer.
[/ QUOTE ]
Q10 only has 1 answer. It could be numerical or T/F.
aloiz
GuyOnTilt
08-02-2004, 08:17 PM
i understand, but basically you are choosing what you want the answer to be.
Only if Q9 is false. If Q9 is true, then Q1 has to have one specific answer.
GoT
aloiz
08-02-2004, 08:18 PM
If you pick an arbitrary number and then go through the rest of the quiz you won't be able to answer all the question (unless you pick the right number). GoT is right about the answer being a perfect square.
aloiz
daryn
08-02-2004, 08:18 PM
what i mean is, you should be able to, upon hearing the answers, ask how you got them.
for instance, if one question is, what is the average of all other answers, and you got 15, i'd like to be shown where you added up all the other answers, divided by the number of questions, etc.
but if i ask, how did you get #1? i would be told, look, it just is.
daryn
08-02-2004, 08:23 PM
and here's another one.. you're saying Q10 can be a T/F answer?
Q: What is the answer to this question?
A: True.
obviously i understand that you might MAKE the answer true or false, depending on what you need for the other things to hold... but i just see this whole thing as a bunch of bullshit trick questions.
aloiz
08-02-2004, 08:26 PM
Yes you make answer to Q10 whatever you need to allow other answers to hold. Although it might seem like the questions are abitrary there is a logical step by step way you can deduce the answers to all the question, although not in the order presented. That's what makes it so hard.
aloiz
daryn
08-02-2004, 08:29 PM
i don't think you understand what i'm saying.
i understand you can't just "pick numbers from the sky" and have everything still work.
i'm just saying, the questions just start to lose all meaning.
for example, if one of the questions was:
What color is a tree?
and you answered
15.
because you "had to" .. it would be a dumb puzzle.
GuyOnTilt
08-02-2004, 08:29 PM
Could you PM me your solutions aloiz so I can see if they get around the contradictions I'm finding? I'm done trying this quiz the way it's currently worded.
Okay, I got your PM and I see what I overlooked:
<font color="white">There are 6 answers that have to be certain answers in this quiz that everybody should be able to get pretty quickly:
1.
2. 2
3. T
4. 2
5. F
6.
7. F
8.
9. T
10.
The rest should be able to be deduced through multi-variable algebraic equations. I didn't solve it because of a combination of 2 things: I only tried perfect squares that were divisible by 6 up through 36 and didn't bother to go higher, and also I ignored the fact that Q8 could be a negative number, thus making Q6 much easier to solve.
Obviously Q10 doesn't matter one bit. It should be the last answer sovled.</font>
Good quiz. /images/graemlins/grin.gif
GoT
RocketManJames
08-02-2004, 08:30 PM
So, I'm trying to tackle this...
I reasoned that Q1 and Q8 must be (4,2), (1,1) OR (1/4, 1/2). I cannot fit any other number pair there such that the two questions mesh correctly. In doing so, I ran into some problems...
The CLOSEST (but incorrect) I got was:
Q1: 1
Q2: 2
Q3: False
Q4: 2
Q5: False
Q6: 1/6
Q7: False
Q8: 1
Q9: False
Q10: -5 1/6
Now, the reason why this is all screwed up is that I got 4 False answers, when Q2 has an answer of 2.
A tricky part of this (in my mind) is the Q2/Q4/Q7 combination. Q4 must have an answer of 1 or 2 (and 0 is not allowed, since the question includes itself in the count). An answer of 3 or higher is too restrictive on the other answers. An answer of 2 forces Q2 to be a 2. An answer of 1 allows Q2 to be a 0 or a 2, forcing Q7's answer.
Am I totally on the wrong track?
-RMJ
GuyOnTilt
08-02-2004, 08:31 PM
Daryn,
Q1 can't just be an arbitrary number. Like I said, if Q9 is True (which is does have to be because of a combination of other questions) then Q1 has one specific solution. You should be able to deduce that it has to be the highest number in the quiz, a perfect square, and divisible by 6. It's not just some arbitrary number. It has to meet a bunch of qualifiers, as does Q8 which is directly connected to Q1.
GoT
GuyOnTilt
08-02-2004, 08:34 PM
Am I totally on the wrong track?
No, you're on the right track. After a little thinking, it's clear that Q2 and Q4 do indeed have to both be 2. So now you know that exactly 2 of the 4 T/F Questions have to be true. Now just figure out which ones have to be True and you'll be lest with an algebra problem.
GoT
daryn
08-02-2004, 08:35 PM
got:
are you even reading my posts???
i UNDERSTAND that you cannot just pick ANY number, but what i'm saying is you're just PICKING a number for a question so that it works.
see my tree example above.
my beef with the quiz is, the answer you are forced to pick to make everything work just doesn't make sense.
forget it by the way, i understand your problem. you guys enjoy it. forget i said anything.
aloiz
08-02-2004, 08:35 PM
Some are right, and some are wrong. Telling you which ones would make it too easy. There's at least 1 true/false question that is wrong, and at least one numerical answer wrong. There are no fractional answers. All numerical answers are integers.
aloiz
jdl22
08-02-2004, 08:35 PM
I'm working on it but got frustrated.
Here are some things I've figured out:
A1 (the answer to question 1) must be strictly positive. It clearly can't be zero since Q8 would then have no valid answer. Clearly A8 = sqrt(A1). Notice that A8 = A1/A8 => A1 = A8^2, A8 = 0. So clearly A1 must be strictly positive.
Because of that, the sum of all other numbered answers (including Q10) must be 0.
Because of that, A6 must be (1/6)*A1 (since there are six numbered answers including A6, and the total sum is A1, A6 = A1/6.
A10 must be negative (and hence A5 is false).
Anybody come up with anything else?
GuyOnTilt
08-02-2004, 08:40 PM
i UNDERSTAND that you cannot just pick ANY number, but what i'm saying is you're just PICKING a number for a question so that it works.
I understand what you're saying too. But instead of thinking of it as picking an answer for Q1 just so the rest of the questions work, think of it as finding THE ONLY solutino for Q1 that will make the rest of the puzzle make sense.
GoT
RocketManJames
08-02-2004, 08:54 PM
Answers in white:
<font color="white">
Q1 : 144
Q2 : 2
Q3 : T
Q4 : 2
Q5 : F
Q6 : 24
Q7 : F
Q8 : -12
Q9 : T
Q10: -16
</font>
Solved using a few simultaneous equations... thanks for the hints.
-RMJ
aloiz
08-02-2004, 08:55 PM
congrats, took me much longer to get it.
aloiz
RocketManJames
08-02-2004, 09:11 PM
Now that Aloiz verified the solution, I'll post my steps.
In white... (in case the message subject wasn't enough).
<font color="white">
As most have deduced, and as GoT pointed out, these answers must be correct:
Q2: 2
Q3: T
Q4: 2
Q5: F
Q7: F
Q9: T
Leaving us with these unknowns:
Q1 : Z^2
Q6 : A
Q8 : Z
Q10: X
1) Z^2 + 2 + 2 + A + Z + X = Z^2 (Sum) =>
A + Z + X = -4
2) (Z^2 + 4 + A + Z + X) / 6 = A (Average) =>
Z^2 / 6 = A (by Eq 1)
3) A = -2Z (by Q9's True Condition)
4) Z^2 / 6 = -2Z (by Eq 2 and Eq 3) =>
Z^2 = -12Z =>
Z = -12, Z^2 = 144, A = 24
5) X = -16 (by Eq 1 and Eq 4)
</font>
-RMJ
jwvdcw
08-03-2004, 02:26 PM
[ QUOTE ]
That was supposed to make it clearer. If it had just been the sum off all numerical answers someone would have inevitably asked if that included the answer to question 1. It does.
aloiz
[/ QUOTE ]
I'm so confused...does it include #1 or not?
Basically, this is what I think it means, tell me if I'm wrong:
(2+3+4+5+6+7+8+9+10)x2
right? Since the part in the parentheses is #1 and then you add #1 in its just doubled.
jwvdcw
08-03-2004, 02:29 PM
[ QUOTE ]
i don't think you understand what i'm saying.
i understand you can't just "pick numbers from the sky" and have everything still work.
i'm just saying, the questions just start to lose all meaning.
for example, if one of the questions was:
What color is a tree?
and you answered
15.
because you "had to" .. it would be a dumb puzzle.
[/ QUOTE ]
I agree...it seems arbitrary to me as well.
pudley4
08-03-2004, 03:09 PM
[ QUOTE ]
[ QUOTE ]
i don't think you understand what i'm saying.
i understand you can't just "pick numbers from the sky" and have everything still work.
i'm just saying, the questions just start to lose all meaning.
for example, if one of the questions was:
What color is a tree?
and you answered
15.
because you "had to" .. it would be a dumb puzzle.
[/ QUOTE ]
I agree...it seems arbitrary to me as well.
[/ QUOTE ]
It is arbitrary - if you look only at that single question/equation. Once you look at all the other questions simultaneously, then you can find the answer.
It's the same idea as this quiz:
1: A + 0 = A
2: B + C + D = 0
3: A/C = B
4: A - B = C
5: D
Obviously A can be anything and it will satisfy the first equation. Once you start plugging it into the other equations, you realize that A can't be just any old number.
(Answer: A=4, B=2, C=2, D=-4)
aloiz
08-03-2004, 03:21 PM
[ QUOTE ]
Basically, this is what I think it means, tell me if I'm wrong:
(2+3+4+5+6+7+8+9+10)x2
right? Since the part in the parentheses is #1 and then you add #1 in its just doubled.
[/ QUOTE ]
If I understand this correctly not quite.
Let x = SUM(all other answers in quize not including #1)
Let y = the answer for number 1.
In order for the question to be answered, namely that the answer to #1 equals the sum of all numerical answers in the quiz including #1 we must satisfy the equation y = x + y. Now if x is not equal to 0 then y must be equal to infinity, however if x does equal 0 then y could be any integer. I did say at some point that all numerical answers were integers, which seemed like a logical inference. Therfore, x must be 0. Hope that helps.
aloiz
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