Math Fun

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

Moderator: Flannel Jesus

Re: Math Fun

Postby Lev Muishkin » Tue Apr 14, 2015 4:41 pm

Like most of these types of things it is poorly worded.
Fact is that either having the knowledge but not the other, alone is simply not enough to choose between the the dates and the 3 line conversation is of no help.

Unless we know the reasons why the 3 line conversation occurs - such as how they know then the problem is insoluble given the information.

There was a similar problem in this site a couple of years ago, about Monks that was equally stupid.

"Science is entirely Faith Based.... Obama is Muslim....Evil is the opposition to life (e-v-i-l <=> l-i-v-e ... and not by accident). Without evil there could be no life.", James S. Saint.
"The Holocaust was the fault of the Jews; The Holocaust was not genocide", Kriswest
"A Tortoise is a Turtle", Wizard
" Hitler didn't create the Nazis. In reality, the Judists did ... for a purpose of their own. Hitler was merely one they chose to head it up after they discovered the Judist betrayal in WW1, their "Judas Iscariot";James S Saint.
These just keep getting funnier.
User avatar
Lev Muishkin
Philosopher
 
Posts: 4037
Joined: Mon Feb 10, 2014 9:58 am

Re: Math Fun

Postby phoneutria » Tue Apr 14, 2015 4:50 pm

May as well post my explanation

I'm wasn't looking very carefully or focusing on it much because of work, so yeah, June 18 makes no sense :)

Albert: there are only 2 daya that don't repeat, and they don't match the month I know, so Bernard can't know the answer.

Bernard: if Albert knows that I don't know the date, then it can't be May or June, because those months have the only numbers that don't repeat. Thus, since I know the day, and Albert ruled out May, it is July 16.


But now that I think of it, why not August 15?

Edit: because Albert then says that he knows it too. The criteria above eliminate all days except for July 16, August 15, and August 17. If Albert now knows it too, it can't be August, since there are still 2 dates to choose from.
Last edited by phoneutria on Tue Apr 14, 2015 5:00 pm, edited 1 time in total.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Lev Muishkin » Tue Apr 14, 2015 4:52 pm

phoneutria wrote:May as well post my explanation

I'm wasn't looking very carefully or focusing on it much because of work, so yeah, June 18 makes no sense :)

Albert: there are only 2 daya that don't repeat, and they don't match the month I know, so Bernard can't know the answer.

Bernard: if Albert knows that I don't know the date, then it can't be May or June, because those months have the only numbers that don't repeat. Thus, since I know the day, and Albert ruled out May, it is July 16


But now that I think of it, why not August 15?


This solution does not work.

"Science is entirely Faith Based.... Obama is Muslim....Evil is the opposition to life (e-v-i-l <=> l-i-v-e ... and not by accident). Without evil there could be no life.", James S. Saint.
"The Holocaust was the fault of the Jews; The Holocaust was not genocide", Kriswest
"A Tortoise is a Turtle", Wizard
" Hitler didn't create the Nazis. In reality, the Judists did ... for a purpose of their own. Hitler was merely one they chose to head it up after they discovered the Judist betrayal in WW1, their "Judas Iscariot";James S Saint.
These just keep getting funnier.
User avatar
Lev Muishkin
Philosopher
 
Posts: 4037
Joined: Mon Feb 10, 2014 9:58 am

Re: Math Fun

Postby phoneutria » Tue Apr 14, 2015 4:57 pm

Oh, I got it... I'll edit my tab above.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Lev Muishkin » Tue Apr 14, 2015 5:02 pm

phoneutria wrote:Oh, I got it... I'll edit my tab above.


However. B knowing that answer can ONLY conclude that June the 18th is the day, as he knows it is the 18th and from the list he can see only one date with that number. On hearing that B knows, A can also conclude that the birthday has to be on the only date that has an exclusive day number. As of all the dates, only one month has a day number not shared with any other month.
Last edited by Lev Muishkin on Tue Apr 14, 2015 5:15 pm, edited 1 time in total.

"Science is entirely Faith Based.... Obama is Muslim....Evil is the opposition to life (e-v-i-l <=> l-i-v-e ... and not by accident). Without evil there could be no life.", James S. Saint.
"The Holocaust was the fault of the Jews; The Holocaust was not genocide", Kriswest
"A Tortoise is a Turtle", Wizard
" Hitler didn't create the Nazis. In reality, the Judists did ... for a purpose of their own. Hitler was merely one they chose to head it up after they discovered the Judist betrayal in WW1, their "Judas Iscariot";James S Saint.
These just keep getting funnier.
User avatar
Lev Muishkin
Philosopher
 
Posts: 4037
Joined: Mon Feb 10, 2014 9:58 am

Re: Math Fun

Postby phoneutria » Tue Apr 14, 2015 5:14 pm

Don't be angry at the problem, levypoo.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Lev Muishkin » Tue Apr 14, 2015 5:16 pm

phoneutria wrote:Don't be angry at the problem, levypoo.


Sorry I'm back in the room.

18th June

"Science is entirely Faith Based.... Obama is Muslim....Evil is the opposition to life (e-v-i-l <=> l-i-v-e ... and not by accident). Without evil there could be no life.", James S. Saint.
"The Holocaust was the fault of the Jews; The Holocaust was not genocide", Kriswest
"A Tortoise is a Turtle", Wizard
" Hitler didn't create the Nazis. In reality, the Judists did ... for a purpose of their own. Hitler was merely one they chose to head it up after they discovered the Judist betrayal in WW1, their "Judas Iscariot";James S Saint.
These just keep getting funnier.
User avatar
Lev Muishkin
Philosopher
 
Posts: 4037
Joined: Mon Feb 10, 2014 9:58 am

Re: Math Fun

Postby phoneutria » Tue Apr 14, 2015 5:32 pm

No no...

A says B can't know the answer, so it can't be any number that occurs only once. 19 and 18 are out along with may and june.

May 15
May 16
May 19
June 17
June 18

July 14
July 16
August 14
August 15
August 17

That clue solves the problem of the month for B, so it had to be a number that repeats for either may or june. july 14 and august 14 are out.

May 15
May 16
May 19
June 17
June 18
July 14

July 16
August 14
August 15
August 17

Knowing that B knows solved the problem for A. Therefore it has to be a date with only one month option.

May 15
May 16
May 19
June 17
June 18
July 14

July 16
August 14
August 15
August 17
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Tue Apr 14, 2015 6:43 pm

All three of you are wrong.

Aug 17
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phoneutria » Tue Apr 14, 2015 6:44 pm

Post your reasoning, james.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Tue Apr 14, 2015 6:54 pm

Given the answer, can't you discover the reasoning?


Edit ... nahh.. never mind .. I boobooed. You're right.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Carleas » Wed Apr 15, 2015 9:02 pm

That's the one, Phoneutria.

Here's another I just came across, I haven't had time to try to figure it out but it looks like fun, and mathier than most problems of this kind.
Sasha Volokh wrote:Two numbers a and b are between 2 and 99. [Note: They’re not constrained to be different from each other. [S.V.]]

Peter is given the product of the numbers, ab (and knows he is given the product).

Sarah is given the sum a+b (and knows she is given the sum).

They also know the numbers are between 2 and 99.

They are UVa math majors, so they are great at math and completely honorable!

Peter says, “I don’t know the numbers.”

Sarah says, “I knew you didn’t know the numbers.”

Peter then says, “I know the numbers now.”

Sarah then says, “Ah ha! I know the numbers now.”

What are the numbers?


This one could take a while.
User Control Panel > Board preference > Edit display options > Display signatures: No.
Carleas
Magister Ludi
 
Posts: 6107
Joined: Wed Feb 02, 2005 8:10 pm
Location: Washington DC, USA

Re: Math Fun

Postby James S Saint » Wed Apr 15, 2015 10:25 pm

Just first shot at it..
nah ... screwed up again
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Sauwelios » Thu Apr 16, 2015 1:52 am

I thought I was well on my way to solving it--I had just reasoned out what I considered the final key to the solution--, when I suddenly realised a very basic fact had escaped my attention. The fact that the numbers are between 2 and 99 means their product cannot be a prime number. But then it's completely superfluous for Peter to say he doesn't know the numbers (which he could, from the information given him, only know if the product was a prime number). But then it's just as superfluous for Sarah to say she knew he didn't know the numbers. For then Peter could have known Sarah could have known he didn't know the numbers! So their saying those things need not give either of them any new information. So if Peter knows the numbers after those things have been said, he could have known them as soon as he was informed of the product. In fact, he would have known them, considering that he's great at math. So the problem has now become completely obscure to me, and I suspect that it doesn't add up.
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)
User avatar
Sauwelios
Philosophical Supremacist
 
Posts: 7182
Joined: Fri Sep 08, 2006 7:07 pm
Location: Amsterdam

Re: Math Fun

Postby Sauwelios » Thu Apr 16, 2015 2:17 am

Sauwelios wrote:I thought I was well on my way to solving it--I had just reasoned out what I considered the final key to the solution--, when I suddenly realised a very basic fact had escaped my attention. The fact that the numbers are between 2 and 99 means their product cannot be a prime number. But then it's completely superfluous for Peter to say he doesn't know the numbers (which he could, from the information given him, only know if the product was a prime number). But then it's just as superfluous for Sarah to say she knew he didn't know the numbers. For then Peter could have known Sarah could have known he didn't know the numbers! So their saying those things need not give either of them any new information. So if Peter knows the numbers after those things have been said, he could have known them as soon as he was informed of the product. In fact, he would have known them, considering that he's great at math. So the problem has now become completely obscure to me, and I suspect that it doesn't add up.


Ugh, I now suppose the above just makes solving the problem require one extra step--an even more tedious one than the one I previously considered the last step. The Washington Post says, "This problem took a little more brute force to solve than seems elegant to me[.]" Here's what I have thus far:

The fact that both numbers are between 2 and 99 means the product cannot be a prime number. The first thing Peter says, then, tells us the product is not a number that can only be divided by one or two other numbers than 1 and itself (for instance, 9 only by 3, and 8 only by 2 and 4).

Drinking some wine with my food also didn't help.
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)
User avatar
Sauwelios
Philosophical Supremacist
 
Posts: 7182
Joined: Fri Sep 08, 2006 7:07 pm
Location: Amsterdam

Re: Math Fun

Postby A Shieldmaiden » Thu Apr 16, 2015 3:04 am

July 16


MOD EDIT: edited to entab the response, so as not to spoil for others - Carleas
The man that walks his own road, walks alone

Old Norse Proverb
User avatar
A Shieldmaiden
Philosopher
 
Posts: 2048
Joined: Mon Aug 25, 2014 6:13 am

Re: Math Fun

Postby phoneutria » Thu Apr 16, 2015 4:18 am

Sauwelios:
It also can't be any product greater than 198.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Sauwelios » Thu Apr 16, 2015 4:37 am

phoneutria, don't you mean the sum?
"Someone may object that the successful revolt against the universal and homogeneous state could have no other effect than that the identical historical process which has led from the primitive horde to the final state will be repeated. But would such a repetition of the process--a new lease of life for man's humanity--not be preferable to the indefinite continuation of the inhuman end? Do we not enjoy every spring although we know the cycle of the seasons, although we know that winter will come again?" (Leo Strauss, "Restatement on Xenophon's Hiero".)
User avatar
Sauwelios
Philosophical Supremacist
 
Posts: 7182
Joined: Fri Sep 08, 2006 7:07 pm
Location: Amsterdam

Re: Math Fun

Postby phoneutria » Thu Apr 16, 2015 4:56 am

lol I read the problem incorrectly, never mind.

Is scripting allowed? Math majors use scientific calculators, right?
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Thu Apr 16, 2015 8:24 am

I can see how he knows from what she said. But I'm not seeing how she could know from what he said.

Suspecting a possible wording issue. But gunna have to ponder this one.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Carleas » Thu Apr 16, 2015 1:39 pm

I'm using excel.
The linked post said that some brute force was involved, so I think it's a question of reasoning about what you're looking for and then finding the things that match those criteria.
User Control Panel > Board preference > Edit display options > Display signatures: No.
Carleas
Magister Ludi
 
Posts: 6107
Joined: Wed Feb 02, 2005 8:10 pm
Location: Washington DC, USA

Re: Math Fun

Postby phoneutria » Thu Apr 16, 2015 3:46 pm

I think the wording in the problem is missing the information that the numbers have to be integers.
They have to, right?
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3401
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Sauwelios » Thu Apr 16, 2015 4:08 pm

phoneutria wrote:I think the wording in the problem is missing the information that the numbers have to be integers.
They have to, right?


I think so.

Also, that the numbers can be 2 and 99 ("between" in the inclusive sense), and that Peter knows Sarah is given the sum and Sarah that Peter is given the product. It seems problems like this are usually poorly worded.


EDIT: Also,
it's implied that it's not required to be able to tell which number is a and which is b, for if it were, Peter would know the numbers as soon as he was given the product.
User avatar
Sauwelios
Philosophical Supremacist
 
Posts: 7182
Joined: Fri Sep 08, 2006 7:07 pm
Location: Amsterdam

Re: Math Fun

Postby Sauwelios » Thu Apr 16, 2015 5:17 pm

James S Saint wrote:I can see how he knows from what she said. But I'm not seeing how she could know from what he said.


That's where I am, too:

The fact that both numbers are between 2 and 99 means the product cannot be a prime number. The first thing Peter says, then, tells us the product is not a number that can only be divided by one or two other numbers than 1 and itself (for instance, 9 only by 3 and 8 only by 2 and 4). The second thing Sarah says tells us that she didn't know the numbers yet when she said the first thing she said. The first thing she said, then, tells us the sum is a number that can be arrived at by multiple sets of two numbers (e.g., 8, by 2 and 6 and by 4 and 4). The second thing Peter says then tells us that the sums of the possible numbers of which he knows the product contain only one number for which that goes (for instance, if the product is 12 the sum can only be 7 or 8, and 8 is the only number of the two for which the aforesaid goes (the product 10 was already precluded by the first thing Peter said)). Now if the numbers are 2 and 6, Peter knows they are as soon as Sarah tells him she knows that he didn't know the numbers (for then the sum must be 8 and not 7).
User avatar
Sauwelios
Philosophical Supremacist
 
Posts: 7182
Joined: Fri Sep 08, 2006 7:07 pm
Location: Amsterdam

Re: Math Fun

Postby Carleas » Thu Apr 16, 2015 6:38 pm

Not the answer, but might reveal more information that people want to know:
I got it with heavy reliance upon Excel tables, formulas, and conditional formatting to simplify the brute force parts. The brute force seems to be inescapable, as the problem statement at the Post suggests.

The answer and how I got there:
Peter's statement that he doesn't know doesn't tell us much. There are actually a lot of numbers that are ruled out immediately:
UniqueProducts.PNG
UniqueProducts.PNG (38.9 KiB) Viewed 1059 times

This is a table of all the possible products (zoomed way out, the big picture is what's important here). Along the top and left are numbers 2-99, and the product of any two numbers is at the intersection of the respective row/column(2x2 is in the upper left, 99x99 is in the lower right). For simplicity, I only filled in the upper half of the table, since the lower half is identical. Cells highlighted in red appear more than once; those in white are unique. From Peter's statement, we know that it's none of the unique values (otherwise he would know immediately), but that doesn't get us very far.

Sarah's statement, "I knew you didn't know" tells us that whatever sum she has, every product of every pair of integers that sums to that is non-unique. If there were two numbers that added to the number she knows, and multiplied to a unique product, then she wouldn't know whether or not Peter knew.
CountofProducts.PNG
CountofProducts.PNG (78.33 KiB) Viewed 1059 times

This table shows the number of times each product appears in the entire set. Red cells appear once, white cells twice, and the bluer the more the appear from there. This chart wasn't necessary, it was the result of what turned out to be a dead end, but it makes it a little easier to see some patterns and it's just s'damn pretty, I didn't want it to go to waste.

For any sum, there will be a diagonal line sloping up and right that has the same sum (because, e.g., 6+5 = 7+4 = 8+3 = 9+2 = 11). So in this chart, I was looking for the sloping lines that don't contain unique values, i.e. that had no reds. This immediately eliminates everthing to the right of the solid red column around the middle of the chart (53xY): every diagonal line that extends beyond that column will have at least 1 unique product, and we need diagonal lines that have no unique products. There are relatively few lines, and we can take the list of sums corresponding to those lines: 11,17,23,27,35,37,41,47,53. We know the sum is one of those numbers.

Peter's next answer tells us that, among the pairs that sum to 11,17,23,27,35,37,41,47, or 53, his number must be unique: if it appeared in two of the diagonally sloping lines, he wouldn't know from Sarah's statement which line it was in, i.e. what the sum of the numbers is. So I made this chart:
UniqueProductsFromSums.PNG
UniqueProductsFromSums.PNG (11.51 KiB) Viewed 1059 times

This shows only the products that correspond to the available sums, and it's highlighted to show duplicates (pink if a number appears more than once, white if not). Peter's number is one of the numbers in white.

Finally, we look at Sarah's last statement. Peter knows because his product is one of the values in white on the previous chart, that is, there is only one combination of numbers that falls along the diagonally sloping lines that has a product equal to the one he knows. This is enough to tell Sarah what number it is only if it is the only value in white with the sum she knows. And if we look along the diagonal lines, we see that 52, at the intersection of 4 and 13, is the only white number in its line (the line of numbers that sum to 17), and that no other line has such a number.

And so, because Sarah knows the answer, we know the answer. QED
User Control Panel > Board preference > Edit display options > Display signatures: No.
Carleas
Magister Ludi
 
Posts: 6107
Joined: Wed Feb 02, 2005 8:10 pm
Location: Washington DC, USA

PreviousNext

Return to Science, Technology, and Math



Who is online

Users browsing this forum: No registered users