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 [quote="HyToFry"]Something else i noticed when i was examining this problem, the product would have to be less than the maximum of the second number, (for any number that would alow Sam to know that Paul Couldn't know) so so a product of >100 wouldn't work and can always be ruled out by both paul and sam anyways, THERE IS ALOT OF TIME INVOLED TO PROVE THIS TO YOURSELF, SO IF YOU WANT TO GO RIGHT AHEAD [img]http://www.greylabyrinth.com/Forums/smile.gif[/img]. So far these are all the criteria i have come up with 1 < x <= y and x + y is not a prime number And x * y < max(y) if the numbers do not meet the third criteria, then paul knows the answer in the first place [img]http://www.greylabyrinth.com/Forums/smile.gif[/img] A good example would be if P = 115 because 5*23 = 115 and 1*115 = 115 and 1,115 is not a possible answer (out of town), Paul would know from the start the answer was 5,23. I haven't done much reasearch on this, however 2,25 meets all the criteria required, also ALL of the products of the sumroots of 2,25 have at least two sumroots that meet thees requirements [img]http://www.greylabyrinth.com/Forums/wink.gif[/img] except 2,25, the only other possible sumroots it could have is 5,10 and since 5,10 dosn't meat these requirements, it can be ruled out. If you find a hole PLEASE let me know. thanx Chaz [/quote]
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Ghost Post
Posted: Fri Mar 17, 2000 5:19 pm    Post subject: 1

The solution is 4,13.
(Don't ask me why, I am tired. I solved it last week, and I admit that I had to write down a program on my PC, because trying with paper and pen I made a mistake and jumped the right sum 17)
Ghost Post
Posted: Fri Mar 17, 2000 5:17 pm    Post subject: 0

The solution is 4,13.
(Don't ask me why, I am tired. I solved it last week, and I admit that I had to write down a program on my PC, because trying with paper and pen I made a mistake and jumped the right sum 17)

------------------
Ghost Post
Posted: Fri Mar 17, 2000 5:07 pm    Post subject: -1

4 13 is the only solution.
don't ask me to write down the reasons!
(I began computation by hand trying the couples adding 11 or 17 or 23 or ... ; I suspected I made a mistake, because my numbers became to grow, so I had to program the problem on my PC (with Mathematica) and I discovered the 4-13 solution; it is not very polite to solve a game with a computer, but I had to do it!)

Ghost Post
Posted: Sat Mar 11, 2000 2:27 am    Post subject: -2

Yes, 2,25 is one of 24 solutions under that interpretation.

I'm confident though that the "official" interpretation of 'forgot' will be that they forgot, with no implication about their ability to figure it out. That is a problematic interpretation were it real life though.

For instance, if Paul knew the two numbers were positive integers, and knew the product to be 1, could he possibly claim that he "forgot" the two numbers? If he knows the size of the town, can he claim to have forgotten the numbers if he knows the product to be 289 (17*17)?

Where is the dividing line between what one can reasonably say they forgot, even though they have enough information to figure it out with some thought, and what one can't resonably say they forgot given how easy it is to figure out from known information?

A brilliant mathematician may claim to have forgotten what the billionth or hundreth prime number is, but not the first, second or third prime number. How about the tenth, or twentieth?
HyToFry
Posted: Sat Mar 11, 2000 2:25 am    Post subject: -3

Okay extro... i have revisited your 3 possible scenerios and discovered that you were almost right, I can now see why "forgot" means just that and "not knowing the size of the town" is a different outcome, but using these two I can only see 3 possible interpertations of the puzzle
So far, I think we have three possible differences in interpretation of the puzzle:
quote:

1) "forgot" means "forgot", or it means "forgot, and can't figure out"
2) They either do or don't know the maximum house number is 100 (for first and second number)

I agree with these statements and this makes three possible outcomes:

1:They did not know the size of town, and "forgot" means just that (if forgot meant forgot and can't figure out it wouldn't matter because either way they couldn't figure it out) anywayz this makes 10 Possible outcomes, (4,13) (4,55) (4,61) (3,64) (4,67) (4,73) (3,76) (4,79) (4,83) and (4,89).

2:The DID know the size of town, and "forgot" means just that and not "forgot and can't figure it out", this makes ONE possible outcome, (4,13) And since we can ASSUME that the puzzle knows we can solve it, although it never says that we can (interestingly enough this is another possible outcome) this is probably going to be the right answer

3:They did know the size of the Town and forgot means forgot and can't figure it out. This makes 24 possible outcomes (2,25) (2,27) (2,42) (2,44) (2,54) (2,58)
(2,82) (3,25) (3,35) (3,45) (3,51) (3,69)
(3,74) (3,86) (4,74) (4,82) (5,35) (5,58)
(6,74) (7,58) (7,62) (10,58) (11,46) and (13,34).

The other criteria you have stated is impossible:
quote:

3) When Sam says "I knew you couldn't figure out the numbers", she means she knew it from the beginning, or she means she knew it just prior to him saying it.
That's 8 possible variations in interpretation. I'll get back with answers for all 8, and it will be settled.

It is IMPOSSIBLE for S to know that P cannot figure out the answer before P makes his first statement. For this to be possible S would have to know that P knows the Product and has forgoten the Address. S doesn't have a clue about this until after P makes his first statement, so for all S knows P could figure it out based off the fact that P may or may not know the Address, and the fact that S doesn't even know that P knows the product until after finding out that P has forgotten the address.

4,13 is the only possible answer in these cases, ASSUMING that the puzzle knows we can solve it (which it doesn't say)

Thanks extro... for all of your help in getting to the bottom of this VIRIS of a puzzle... YOU ROCK!!!!!!!!!!!!!!!!!

oh ROCKING is a good thing (just thought i would throw that in, just in case English isn't your first langauge.

[This message has been edited by HyToFry (edited 03-10-2000).]
HyToFry
Posted: Sat Mar 11, 2000 12:20 am    Post subject: -4

AHA!!!!!!!!!!!!!!!!!!!!!!! I GET IT .

However keep in mind that you are ASSUMING that Paul saying "forgot" means just that, and not "forgot and can't figure out", while at the same time you are ruling out the chance that Paul and Sam just happend to see the party. (which is about as far fetched).

Also you are Assumeing that Paul and Sam know the size of the town, "which it never says that it does", and third you are assuming that the puzzle knows that we can figure out the answer based on the information givin, however it never says this .

One other thing i noticed while takeing this puzzle TOTALLY literaly is this:
Paul never says in step one that he HAS forgotten the address, only that he is afraid that he forgot it, which isn't to say that he has, so Paul may have realized that he didn't forget it and Sam may have just rememebered.

So in conclusion i still think the puzzle should be more specific... and I'm pretty sure that you will agree.

Oh and one more thing, You agree that 2,25 is still a possible answer if forgot means forgot and can't figure out, and P and S know the size of the town right? (this will make me feel alot better just knowing that you agree with this one statement)

[This message has been edited by HyToFry (edited 03-10-2000).]
Ghost Post
Posted: Sat Mar 11, 2000 12:01 am    Post subject: -5

"TOP OF PAGE"
YOU HAVE TO BE KIDDING!!!

Again, if it were 4 and 55, Sam would know the sum to be 59.

Paul says (his second statement), and I quote, "I can't figure out where the party is". He says this knowing the numbers are greater than 1 (fact) and no greater than 100 (same assumption as always, which leads to 4,13 as answer).

Samantha says "I knew that".

So, with the sum=59, she supposedly already knew (knowing only the sum, and that they both know both numbers are in the range 2..100, with the first <= the second) that Paul could not figure out the numbers.

Yes, I assume his first statement ("I forgot") means just that. But his second statement ("I can't figure out") means he can't figure it out.

If the sum were 59, how could Sam know that Paul couldn't "FIGURE OUT" the numbers, as he would be able to if the numbers were 6 and 53.

Again, after the first two statements (Paul and Sam saying "I forgot"), we (and THEY) know this:
A) 2 <= first <= second <= 100
B) Paul knows value of first*second
C) Sam knows value of first+second

NOW, AT THIS POINT, Sam knows that Paul "CAN'T FIGURE OUT" the numbers. She has not said so yet, but when she does (right after Pauls next statement), THIS is the point in time she is referring to! Paul will now say, and I QUOTE, "I can't figure out where the party is", to which she replies "I KNEW that". She knew it before he said it. She knows it NOW.

If the sum were 17 (4+13), this would be true. The only possible products (2*15, 3*14, 4*13 ... 8*9) ALL have multiple factorizations into first*second with in the range 2..100, with first<=second. She would know that Paul "CAN'T FIGURE OUT" the numbers (knowing fact A above, and any of the possible products 30, 42, 52, ... 72).

If the sum were 59 (4+55), this would be false, because 59 can be 6+53, and 6*53=318 HAS ONLY ONE FACTORIZATION given the constraints of fact A above, which fact Paul is well aware of (SAME ASSUMPTION as for 4,13). If the sum were 59, the product might be 318 (6*53), from which Paul could "FIGURE OUT" (given that he knows fact A above, which is THE SAME ASSUMPTION used for the 4,13 case) that the numbers are 6 and 53.

See the light? If not, goto "TOP OF PAGE".
If so, say "AHA!"

[This message has been edited by extro... (edited 03-10-2000).]
HyToFry
Posted: Fri Mar 10, 2000 10:54 pm    Post subject: -6

No your wrong in the case that :
Quote:
Assuming "I forgot" means only that, and not also "I can't figure it out", and assuming they know the size of the town

4,55 is still a possible number, something you said earlier proves this:
quote:
Here's the problem with (4,55)
If it were 4 & 55, Samantha knows the sum is 59. She can't discount the possibility that the numbers might be 6 & 53, in which case Paul would know from the product (6*53=318) that the numbers are 6 and 53. But she claims to know that Paul could not know the numbers.

Note: 318 = 6*53 = 3*106 = 2*159, but 106 and 159 are both over 100. If Paul knew the product to be 318, he would know the numbers are 6 & 53.

In this case you are assumeing that he forgot means just that, and not "forgot and can't figure it out", so 4,55 still fits the bill.

And besides all that Saying that forgot means just that and not forgot and can't figure it is about like saying the following (takeing EVERYTHING that paul says to be literal)

Paul: I'm afraid I've forgotten the address. I can only remember the product of the two numbers, and that the first number wasn't greater than the second.

By saying I can ONLY remember the product and that the first wasn't greater than the second, paul is stateing that ALL other information in the world has been drained from his mind (this includes adding, subtracting, multiplication, division, his name, why he needed to know the address, sams name, what country he lived in EVERYTHING.)

Now you see why i think that saying forgot means only forgot, and not forgot and can't figure out.... Is a rediculas (at best) statement........ I hope

[This message has been edited by HyToFry (edited 03-10-2000).]
Ghost Post
Posted: Fri Mar 10, 2000 10:38 pm    Post subject: -7

You're kidding, right? Is that the light you're asking whether I see? That you're just jerking us around?

It is no longer at all clear what point you are arguing.

Assuming "I forgot" means only that, and not also "I can't figure it out", and assuming they know the size of the town, then the only answer is 4,13.

It can't be 2,26, because Sam wouldn't be sure it isn't 5,23, in which case Paul WOULD know the numbers from the product (115). So 2,26 is NOT possible, because Sam knows the numbers are NOT 5,23. How could she know that if she only knows the sum (28)???

Do you agree?

HyToFry
Posted: Fri Mar 10, 2000 9:53 pm    Post subject: -8

bradan said it best in one of his posts:
quote:
(4,61), (16,73), (64,73) are not possibilities here because of the current size of the village!
If (4,61) was the address, => P=244. The only other possible address for P=244 is (2,122) which is not an address in the village. Therefore, Paul would get the address straight away. [unless of course he also forgot the size of the town!]

The same occurs for the possibility of:

(16,73):
P=1168 => other addresses are (4,292) & (2,584)... not in the village.

&(64,73):
P=4672 => other addresses are (16,292), (8,584), (4,1168), (2,2336)... also not in the village.

He proves my point with one sentance:
Quote:
If (4,61) was the address, => P=244. The only other possible address for P=244 is (2,122) which is not an address in the village. Therefore, Paul would get the address straight away. [unless of course he also forgot the size of the town!]

the same would be true if he never knew the size of the town, or if he did, but saying that "forgot" means he forgot and not that he forgot and couldn't have figured it out.

However braden missed the fact that 4,13 acts EXACTLY the same way. because of the problem with the answer being 3,25 and 11,17, UNLESS PAUL FORGOT, OR DIDN'T KNOW THE SIZE OF THE TOWN, 4,13 is not a possible answer.
HyToFry
Posted: Fri Mar 10, 2000 8:52 pm    Post subject: -9

This is true, but also true for 2,26 (the other half of 4,13)

2+26 = 18 which has only two sets of prime numbers that can add up to it, 5,23 and 11,17

5*23 = 115 and so paul would know that it was 5,23 (as it couldn't possibly be 1,115) so sam can rule this number out.

11,17 works the same

since there is no other set of primes that can add up to 28 Sam would KNOW that Paul couldn't know the answer... (the reasoning is the same as it is for 4,55) it would be like saying that sam didn't know that paul might think the answer was 1,318. (the other set of 6,53)

See the light yet?

[This message has been edited by HyToFry (edited 03-10-2000).]
Ghost Post
Posted: Fri Mar 10, 2000 8:42 pm    Post subject: -10

They both knew from the start that the town was a 100 by 100 grid.

Paul says "I forgot, but know the product, and that first is not greater than second".

Sam says "I forgot, but know the sum, and that neither is one"

Sam at this point (before his next statement) knows that Paul can't figure out the numbers. If the numbers were 6 and 53, he could figure it out now. If the sum were 59, Sam couldn't know what she does. So the sum is not 59, and the numbers can't be 4 and 55.
HyToFry
Posted: Fri Mar 10, 2000 8:00 pm    Post subject: -11

Extro... you found three, however there is really only one difference.

quote:
So far, I think we have three possible differences in interpretation of the puzzle:
1) "forgot" means "forgot", or it means "forgot, and can't figure out"
2) They either do or don't know the maximum house number is 100 (for first and second number)

1 and 2 have the same outcomes either way.
so they are basically the same, (either they did know the size, but couldn't figure it out) or they could have figured it out if they had known the size, if they couldn't figure it out, and didn't know the size it wouldn't matter.

Quote:
3) When Sam says "I knew you couldn't figure out the numbers", she means she knew it from the beginning, or she means she knew it just prior to him saying it.

We konw that she knew this from the begining because paul telling her that A<=B doesn't help her figure this out, so it doesn't matter how you interperate this, either way the outcome is the same

Now we're back to only one variation.

Extro 4,55 still stands if criteria 2 (or 1) is met

Quote:
Note: 318 = 6*53 = 3*106 = 2*159, but 106 and 159 are both over 100. If Paul knew the product to be 318, he would know the numbers are 6 & 53

he WOULDN'T know this because he wouldn't know the maximum house size was 100 (or if you would like to say it the other way, he didn't say he couldn't have figured it out.

If 4,13 is possible then so is 4,55 and if not then 2,25 is possible and 2,27 etc....

[This message has been edited by HyToFry (edited 03-10-2000).]
Ghost Post
Posted: Fri Mar 10, 2000 7:35 pm    Post subject: -12

HyToFry: The problem with 4,55 still stands. Pauls first statement is that he forgot the two numbers. His second statement is that he can't figure them out (knowing their product and that they are in the range 2..100).

If the sum were 59, Samantha could not have known the numbers were not 6 and 53 before Pauls second statement, thus could not have known that Paul could not figure out the numbers (as he would be able to do if they were 6 and 53). So 4,55 is no good - Samantha's second statement wouldn't be true.

So far, I think we have three possible differences in interpretation of the puzzle:
1) "forgot" means "forgot", or it means "forgot, and can't figure out"
2) They either do or don't know the maximum house number is 100 (for first and second number)
3) When Sam says "I knew you couldn't figure out the numbers", she means she knew it from the beginning, or she means she knew it just prior to him saying it.
That's 8 possible variations in interpretation. I'll get back with answers for all 8, and it will be settled.
HyToFry
Posted: Fri Mar 10, 2000 7:10 pm    Post subject: -13

Also, looking through the other topics, I noticed a flaw in your thinking as well:

Gidon Wrote
quote:
Hi
I looked at the old thread aswell, and wrote a program to generate the numbers. I correctly get the numbers 4,13, but also get the numbers (4,55) (4,61) (3,64) (4,67) (4,73) (3,76) (4,79) (4,83) (4,89)

any comments? the way the puzzle was phrased i hoped to find a unique sollution. the program is in PERL (61 readable lines), and if anyone wants it leave your email and request in this thread.

Cheers

Gidon

In response to this Extro... wrote:

quote:
Here's the problem with (4,55)
If it were 4 & 55, Samantha knows the sum is 59. She can't discount the possibility that the numbers might be 6 & 53, in which case Paul would know from the product (6*53=318) that the numbers are 6 and 53. But she claims to know that Paul could not know the numbers.

Note: 318 = 6*53 = 3*106 = 2*159, but 106 and 159 are both over 100. If Paul knew the product to be 318, he would know the numbers are 6 & 53.

Now that we have all been enlighted as to the fact that Paul said he had forgotten (and not that he couldn't have figured it out) 4,55 IS STILL A POSSIBLE ANSWER
You have all said so yourself...

so either way if P and S know the size of the town, or even if they don't there is STILL multiple answers that will fit the bill..

I haven't tried any of Gidon's others answers but I wouldn't doubt that all of his numbers work

So in conclusion:

There are at least two possible outcomes if they know the size of the town, and at least two possible outcomes if they don't know the size. (or can/can't figure out the answer in the first step).

There is a possible of 34 answers to this question.

Either way the question is flawed and it's not just that I interperated it wrong.

Oh and P.S. I'm changeing my answer back to 2,25 - because Like i said i live right next store in 2,24, so i knew this from the start.

Oh and before i forget, extro... i'm not saying your wrong (in fact just the opposite) you were just the only one who pointed out why 4,55 is not possible, which interestingly enough is the same reason that 4,13 is not possible (assuming that they know the size of the town).

So in the end nobody was right, the question was wrong .

I'm sure glad we FINALLY got to the bottom of this

[This message has been edited by HyToFry (edited 03-10-2000).]
HyToFry
Posted: Fri Mar 10, 2000 6:33 pm    Post subject: -14

Array you said
quote:
Well, congratulations on finally getting the correct answer then, even if all the help everyone tried to give you apparently didn't amount to anything (LOL)..
The problem states that P and S are able to deduce the address of the party solely from the information they exchange in the dialog. It does not state that they know the limits of the city. If you assume that they know that the city is 100x100, then perhaps there are multiple answers, but that doesn't show the question is ambigious, it shows that your assumption is wrong.

If this is the case, then the whole riddle doesn't work... you assume things to with your deduction of 4,13
2. You assume that P and S know all of the Prime numbers.
It never states that P and S know all of the prime numbers (and they would have to to know the answer to the puzzle, or if they didn't then P would have to be able to add and S able to multiply).

It does say they are "quick witted" but i think if they were quick witted then P would DEFINATELY know that 1,115 could not be in the town, and S would know this (eliminating the possibility that it could be 3,25) So S still knows that knowing neither number was one would help P. and so P will determan that 2,26 is still possible.

Also we assume that they did figure out the answer at the end (it doesn't say that they figured it out, only that they now know the answer), if we can assume nothing, then how do we know that they didn't just SEE the house? in other words.. Some things HAVE to be assumed in order for the puzzle (in its current form) to be solved at all

Ghost Post
Posted: Fri Mar 10, 2000 5:06 pm    Post subject: -15

HyToFry wrote: Stateing that the problem (never?) says that P only forgot the answer, and not that he couldn't figure it out is pretty far fetched.

OK. If you take "I forgot" (as stated in problem) to mean "I forgot, and I can't figure it out from the information I have available", then you get the 24 possible solutions, one of which is 2,25. Any one of these 24 would allow Paul and Samantha to figure out the exact address from the conversation, although we, from overhearing the conversation, but knowing neither the sum nor product, can't tell exactly which house it is.
HyToFry
Posted: Fri Mar 10, 2000 4:36 pm    Post subject: -16

Okay if P has a product of 52, then his possible root sums are 1,52 (which is eliminated by S in the 2'nd statement) 2,26 and 4,13

Consider S = 28

All of the products of the root sums of 28 have AT LEAST two possible productroots.

Consider 3,25
3*25 = 75, also 5,15 is 75
All numbers that add up to 28 are the same (do the math yourself)

The only exceptions are 5,23 and 11,17 Which P would Know that S would Know that if it was either of these numbers P would know the address from the begining, (Stateing that the problem never says that P only forgot the answer, and not that he couldn't figure it out is pretty far fetched) So because S would know S would have imediantly ruled these out, Due to the fact that P would know the answer in round one. With this in mind I have eliminated the other two possiblities and since all other possibles have multiple product roots, YOU GET THE PICTURE I'M SURE.

Now P would know that S would know this, so either way S=28 or S=17, S would know that P can't possibly be helped with the knowledge that niether number was 1, and so either way S's statement remains true...

When P said I still don't know
and S said I already knew that
P could have said at this point "But did you know that i knew you would know that?"
(because he did)

Ghost Post
Posted: Fri Mar 10, 2000 1:58 pm    Post subject: -17

First, a clarification: You wrote
"when S and P know the size of the town, there are 24 possible outcomes"

I never considered the possibility that they don't know the size of the town. I got the 24 solutions (including 2,25, but not 4,13) when I assumed that the first two statements by Paul and Sam, that they can not remember the address, meant also that they could not figure it out. I assumed they knew the size of the town.

Now, I'm still having trouble parsing your explanation of what is wrong with 4,13.

Paul knows the product is 52, but can't figure out if the numbers are 4,13 or 2,26. (He DOES already know it isn't 1, 52, because Sam already said both numbers were greater than 1)

Sam knows the sum is 17, which could mean the numbers are any of (2,15) (3,14) (4,13) (5, 12) (6, 11) (7, 10) (8, 9). For any of these, the product can only be factored one way. So she knows from the sum that Paul didn't know the numbers.

On the other hand, if she had known the sum to be 28, she would have to consider that the numbers might be (5,23) or (11,17), in which case Paul WOULD have known the numbers from their product. 5*23 = 115 = 1*115, but Paul ALREADY KNEW that neither number was 1 (the size of the town would have also clued him in, but it is not essential here). So, if the sum were 28, Sam could not have known that Paul couldn't figure out the numbers from the product.

So, when Sam say's she knew he couldn't figure it out, that eliminates 28 as the sum, which eliminates 2,26, which leaves only 4,13 as possible numbers with the product 52.

I think I know what you did though. When Samantha says "I knew you couldn't figure out the address", the question is: WHEN did she know? I am assuming she meant she knew that prior to him stating it, but after he was told by her that neither number was a 1. In other words:

1) Paul say's he knows the product, but can't remember the numbers.
2) Sam say's she knows the sum, can't remember the numbers, but remembers neither was a 1.

At this point, Paul knows neither number was a 1, and at this point, Sam knows Paul can't (even with knowing that neither number was a 1) deduce the numbers, but Paul doesn't know she knows that.

3) Paul says he can't deduce the numbers.
4) Sam say's she knew that.
5) Paul - Now I do.
6) Sam - So do I.
araya
Posted: Fri Mar 10, 2000 8:28 am    Post subject: -18

Well, congratulations on finally getting the correct answer then, even if all the help everyone tried to give you apparently didn't amount to anything (LOL)..

The problem states that P and S are able to deduce the address of the party solely from the information they exchange in the dialog. It does not state that they know the limits of the city. If you assume that they know that the city is 100x100, then perhaps there are multiple answers, but that doesn't show the question is ambigious, it shows that your assumption is wrong.
HyToFry
Posted: Fri Mar 10, 2000 3:01 am    Post subject: -19

Extro... you wrote:
quote:
Paul: I'm afraid I've forgotten the address. I can only remember the product of the two numbers, and that the first number wasn't greater than the second.

This just tells us Paul knows first*second, and that first<=second. So we eliminate all solutions with first>second.

Now according to your calculations, which are correct, the numbers cannot = 4,13

4*13 has a product of 52 and 2,26 is the only other set of numbers that have this product...

NOW with 2,26 if paul knows that q<=p<=100, and the only numbers that have only one possible outcome that can be added up to get 28 are 5,23 and 11,17, and all other numbers that can add up to 28 have multilpe sumroots (they do i checked them) THEN then the prime roots would have to be 5,23 or 11,17, BUT because 5*23 = 115 and 1,115 is the other possibility in this scenerio, Sam would be able to rule out the possiblility of 5,25 being the answer, because if it was Paul would know that 5,25 is the answer (because he would have a sum of 115 and 1<=115<=100 is not a true statement and Paul would know this from the start, but he didn't and Sam knew that, so she could rule it out... GET IT?

The same is true for 11,17 although i'm not going to calculate it out for you.

So as far as Paul knows the answer could still be 2,26 - because all other roots of 28 have multiple answers that can be the answer, and thus wouldn't be able to tell if Sam thought the Sum was 28 or 17 as both would let sam know that all possible roots have products with multiple roots

So this goes back to my former statement, IF Sam and Paul DO know the size of the town the answer CANNOT be 4,13 and as you (extro) have pointed out this would result in 24 possibilities, However if they DON'T know the size of the town, 4,13 is the only possible answer.

this is why i have decided to go with 4,13 and its not because of ANYTHING ANYONE HAS SAID that changed my mind (with the exception of Extro... who showed me that when S and P know the size of the town, there are 24 possible outcomes).

[This message has been edited by HyToFry (edited 03-10-2000).]
Ghost Post
Posted: Fri Mar 10, 2000 2:49 am    Post subject: -20

HyToFry: I get 4,13 WITH the assumption that they know the size of the town.

Here's how. I wrote a program which considers possible solutions - initially 10000 possible solutions (I assume they both know both numbers <= 100.) - and eliminates whichever it can based on provided information.

Paul: I'm afraid I've forgotten the address. I can only remember the product of the two numbers, and that the first number wasn't greater than the second.

This just tells us Paul knows first*second, and that first<=second. So we eliminate all solutions with first>second.

Samantha: I've forgotten it too, but can only remember the sum of the two numbers, and that neither number was 1.

This just tells us that Samantha knows first+second, and that first>1 and second>1. So we eliminate all solutions with a 1 in them.

Paul: I can't figure out where the party is.

Now we know that there is more than one way to express the product as p*q while sticking to the above constraints (2<=p<=q<=100). So we can eliminate all pairs having a product that has a single valid factorization.

Samantha: I knew that.

This tells us that the sum is such that any two numbers in the range 2..100 that add up to that sum have a product with more than one valid factorization. So we eliminate all pairs having a sum that can be the sum of two numbers whose product has a single valid factorization.

Paul: OK, I know where the party is.

Now, from the pairs of numbers we have not yet eliminated, some have products with unique factorizations into pairs of numbers we have not yet eliminated. These we keep. All others we eliminate.

Samantha: OK, so do I.

Now, again from the pairs of numbers we have not yet eliminated, some have the same sum as other pairs, and the rest have unique sums. We keep the ones with unique sums.

You are left with 4,13

[This message has been edited by extro... (edited 03-09-2000).]
HyToFry
Posted: Fri Mar 10, 2000 2:14 am    Post subject: -21

Okay I think i should post this before someone else does, I would like to change my answer to 4,13 (which was my second choice untill I discovered the odd 5,23 and 11,17 problem, so i figured that minotaur was trying to trick us to thinking that the answer was 4,13 by limiting the playing field to 100,100 (AND I WASN'T ABOUT LET MINOTAUR TRICK ME AGAIN )

HOWEVER the problem with the problem is that IT NEVER SAYS THAT SAM AND PAUL DO OR DON'T KNOW THE SIZE OF THE PLAYING FIELD. I still think worms theory on Paul not being able to figure out the sum is kinda far fetched .

I am changing my answer to 4,13 ONLY because if Sam and Paul DO know the size of the town then there is 24 different addresses that can fit the criteria, and if they don't know the size of the town there is only 1 4,13 (my girlfriends house, no wonders i couldn't sleep) and I knew that we had to be able to answer the question, thus telling us that Sam and Paul DIDN't know the size of the town....... I WOULD LIKE TO GO ON PROTEST THAT THIS INFORMATION SHOULD BE GIVIN IN THE RIDDLE THOUGH
HyToFry
Posted: Fri Mar 10, 2000 1:08 am    Post subject: -22

My final answer for this riddle is 2,25.

I do however have new reasoning behind this, you see you people may not know this, but i live in Mathematica and my address is 2,24, now i live one house west of 2,25 and those darn kids kept me up all night with their loud music, and times tables. In fact it got to the point where i had to call my girlfriend (who incendently lives at 4,13) and stay the night at her house. (this is how I know that it wasn't at 4,13).

There was a party at 4,13 however I don't rememeber ANY one with the names Sam or Paul attending the party, (in Mathematica we also refer to all people by where they live, ie my name is not HyToFry it is 2,24-3 my Dad(2,24-1) and Mom(2,24-2) have lived here pretty much their whole life, and when I save up enough money, I'm moveing out of this God-Forsaken Town (the reason i hate it so bad, is because whenever there is a town meeting, i have to walk CLEAR down to 1,1 because there is never enough parking for everyone, they couldn't have town square at 50,50, NO thats 50,50-1's house.. oh sorry 50,50-1 in joe parker, he just moved here a month or so ago....

Well i hope this clears things up for you people .

[This message has been edited by HyToFry (edited 03-09-2000).]
HyToFry
Posted: Fri Mar 10, 2000 12:23 am    Post subject: -23

Okay extro you win I have tried a few of the numbers that you posted and have come to the conclusions that ALL of them that I tried hold true for as far as i can tell

This means that either A the puzzle was stated incorectly ie the town should have been 100 by 100+ or B there CAN and IS multiple answers

Or C (posted later) Worm is correct with his theory that Paul Forgot the number, which doesn't mean that he couldn't have figured it out in steps 1 and 2 if it was the product of two primes, and also that Sam wouldn't have thought that Paul could have figured it out in steps one or two, so consider that S = 28, Sam would think that Paul might think the Products of 5,23 (115) could be either 5,23 or 1,115 and because for all she knew her telling him that it can't be 1 would have ruled out the 1,115 and Paul would have known the answer given the information that neither number was 1, she can't rule out the fact that Paul, A VERY QUICK WITTED MATH-MATITION, Wouldn't have been able to figure out that 1,115 is somewhere in Pleasentville the neihboring town, and so she wouldn't know that he couldn't know.
Also Paul would have to assume that Sam wouldn't count on him being smart enough to know that 1,115 is not a possible address.

But if this is the Case, i don't see how paul could possibly know that his products must not be the sum of two primes (unless he is absent-minded) , i mean come on it doesn't take logic to know that 1,115 isn't possible, just common sense , so she couldn't count on the fact that Paul might have just Remembered the address all of the suddon, and she shows up at 4,13 when the party was really over at 6,11 - where Paul is because he happend to remember the address.

(Think about guys it never says that Paul Didn't Just Remeber the address all of the suddon)

This sounds a little far fetched to me though.

My guess is the problem is A (the puzzle was stated incorrectly)... hehe

[This message has been edited by HyToFry (edited 03-09-2000).]
HyToFry
Posted: Fri Mar 10, 2000 12:12 am    Post subject: -24

RIGHT!!!!!!!!!! HEHE

Ghost Post
Posted: Fri Mar 10, 2000 12:08 am    Post subject: -25

HyToFry: 27 a prime? I'd like to see a proof.
HyToFry
Posted: Thu Mar 09, 2000 11:30 pm    Post subject: -26

extro... I have looked at your 2,27 and can prove it wrong

(2,25) - I can't prove the correct answer wrong

(2,27) - Both primes so P would know after S told him A and B > 1

I didn't have time to do any others, as they all meet my criteria for a winning number, but this dosen't mean that all of their roots meet the criteria
HyToFry
Posted: Thu Mar 09, 2000 10:56 pm    Post subject: -27

The reason i know its not 4,13 is because when i was typing up my explanation of why it HAD to be 4,13 I proved that it couldn't be 4,13 I also typed up why it was 2,9 but later proved that wrong, nobody has presented any solid evidance that 2,25 is wrong though, or if the have, I have proved them wrong, so I'm gonna stay with 2,25 for the time being
HyToFry
Posted: Thu Mar 09, 2000 10:22 pm    Post subject: -28

I've said it once, and i'll say it again

Yes accept that he says, "I still can't figure out the answer" after she tells him that is greater than 1, so we know at that point that P can't equal 5*23 or 11*17, because P WOULD be able to figure out the answer at this point, and it stated that both P and S were being Honest about the whole thing
2,25 works Man try it, i'm not sure about all of the other that extro posted

Ghost Post
Posted: Thu Mar 09, 2000 10:18 pm    Post subject: -29

I'm back with 4,13, based on worm pointing out that the first two statements don't say that Paul and Sam can't figure out the numbers, but only that they don't remember them. One could argue about what that means. Can you remember a number is equal to 2+2, and not remember what the number is? So:

1) P says - I don't remember, but the first was not greater than the second.
2) S says - I don't remember, but neither was 1.
3) P says - I can't figure them out.
4) S says - I knew that you couldn't.
5) P says - I now know the numbers.
6) S says - I now know the numbers.

So after statement 2, we (and they) know that the numbers p and q are such that p<=q, 2<=p<=100, and 2<=q<=100
HyToFry
Posted: Thu Mar 09, 2000 10:03 pm    Post subject: -30

Quote:
Sorry, Charlie, Paul DID know that 1 was out of the question when he told Samantha that he couldn't solve.

But not Before she told him which is where you imply that he would have to know it .
HyToFry
Posted: Thu Mar 09, 2000 10:01 pm    Post subject: -31

Yes accept that he says, "I still can't figure out the answer" after she tells him that is greater than 1, so we know at that point that P can't equal 5*23 or 11*17, because P WOULD be able to figure out the answer at this point, and it stated that both P and S were being Honest about the whole thing

2,25 works Man try it, i'm not sure about all of the other that extro posted

[This message has been edited by HyToFry (edited 03-09-2000).]
worm
Posted: Thu Mar 09, 2000 10:00 pm    Post subject: -32

Sorry, Charlie, Paul DID know that 1 was out of the question when he told Samantha that he couldn't solve.
worm
Posted: Thu Mar 09, 2000 9:55 pm    Post subject: -33

I think I see the gap that separates us HyToFry.

In his first statement, Paul did not say that he couldn't figure out the address. He said he had forgotten it, but remembered the product. He doesn't actually tell Samantha that he can't figure it out until after she says she knows the sum and that there are no 1's. But she knew it before he told her, b/c she knew that the sum could not be derived from two prime numbers.

You trackin'?
Ghost Post
Posted: Thu Mar 09, 2000 9:47 pm    Post subject: -34

Missed that about Paul not knowing the numbers were greater than 1 until Sam said so. With that taken into account, I get 24 different solutions:
(2,25) (2,27) (2,42) (2,44) (2,54) (2,58)
(2,82) (3,25) (3,35) (3,45) (3,51) (3,69)
(3,74) (3,86) (4,74) (4,82) (5,35) (5,58)
(6,74) (7,58) (7,62) (10,58) (11,46) (13,34)

I sure hope that the "official" solution doesn't dismiss the subtle variations between this puzzle and the more common variations (such as where 4,13 is the answer).
HyToFry
Posted: Thu Mar 09, 2000 9:40 pm    Post subject: -35

Worm Wrote:
quote:
Explaining is always the tough part.

1. B/c S. knew that P. couldn't solve at first, the sum must be a number that can't be formed from 2 prime numbers (11, 17, 23, 27,29, etc.).

Your assumeing that P knew neither of the numbers could be one, which He didn't, he only knew that B > A, he didn't know that B and A > 1 until after S told him, so S cannot rule out primes as the answer because for all S knew it was the prime numbers, take s = 9
A = 2 and B = 7, both primes
S knows that A <= B but dosn't know if paul is thinking it could be 2,7 OR 1,9, so when she says neither number is 1, that might help Paul to know that it was 2,7

Oh and i still think 2+2 = 17.453445434
HyToFry
Posted: Thu Mar 09, 2000 9:29 pm    Post subject: -36

I have relooked at throsby's criteria that would produce a winning number, and although he was close, he was slightly off....

quote:
a.b cannot be a prime (ruled out by a and b both greater than 1).
a.b cannot be the product of two primes, or else P would know the address.
a+b cannot be the sum of two primes, or else S could not know that P did not know the address.
However, as the fact S knew that P did not, P can then work out that a+b is not the sum of two primes. This means that a.b is a number that has only one set of two factors that add to a number which is not the sum of two primes.
My back of the envelope calculations give me 18 as the first a.b to satisfy this condition, and 2.9 as the address. I have not ruled out all other addresses (I will leave that to people who are either not at work, or much faster at this than I).

There is an exception to rule "a+b cannot be the sum of two primes, or else S could not know that P did not know the address." a+b CAN be the sum of two primes if A*B = a number that is greater than the MAX(B), because the other number of the two primes would be 1 and A*B which is outside of the town, and P would still know the answer from the start....

I hope this clarifys my point that the answer MUST be 2,25.
A = 2, B = 25, S = 27, P = 50
HyToFry
Posted: Thu Mar 09, 2000 9:14 pm    Post subject: -37

Sorry Extro... I already gave this a run for its money

quote:

The answer is 2,8 (product=16, sum=10)
Paul wouldn't know from product. It could be 2,8 or 4,4.

Sam wouldn't know from sum. It could be 2,8 or 3,7 or 4,6 or 5,5, but she eliminates 3,7 and 5,5 from the fact that Paul does not know the numbers.

At this point Paul might think it was 3,7 OR 1,21 and 5,5 or 1,25 respectively..., because Sam dosen't tell him that neither number is one until AFTER, so if it were 2,8 Sam WOULDN'T KNOW that paul Couldn't Know......

Your thinking ahead of the puzzle, you have to wait for Sam to tell him that it can't be 1 for your statement to be true.

It's 2,25 why can't you people just believe me? :b

(I hope)

I'm still waiting for someone to either prove me wrong, or prove 4,13 right?

[This message has been edited by HyToFry (edited 03-09-2000).]
Ghost Post
Posted: Thu Mar 09, 2000 9:02 pm    Post subject: -38

The answer is 2,8 (product=16, sum=10)

Paul wouldn't know from product. It could be 2,8 or 4,4.

Sam wouldn't know from sum. It could be 2,8 or 3,7 or 4,6 or 5,5, but she eliminates 3,7 and 5,5 from the fact that Paul does not know the numbers. That leaves 2,8 and 4,6.

Paul still doesn't know. If it were 4,4, Sam would know the sum to be 8, and would have been considering 2,6 and 4,4 as possibilities- i.e. more than one possibility. So Paul can't eliminate the 4,4 possibility yet.

Sam knows that Paul didn't know. It can't be 4,4 then. If it were 4,4, Sam would have to consider that the numbers are 3,5, and that Paul would know them from the product 15.

Paul now knows it couldn't be 4,4, and so is 2,8.

Sam (recall she was last considering 2,8 and 4,6 from knowing the sum of 10) now knows it is not 4,6 (because 4*6 = 2*12 = 3*8).

A note about the 4,13 solution: 4,13 is a solution to a variant of this puzzle. The puzzle as stated is has the following statements being made:
1) P says I don't know.
2) S says I don't know.
3) P says I don't know.
4) S says I knew that you didn't.
5) P says I now know.
6) S says I now know.

Leave out statements 1 and 2, and the solution is 4,13. But With statements 1 and 2, it's quite different.