Can anyone figure this out?

[DrPizza]

Originally posted by: lexxmac

Originally posted by: DrPizza

I ran the game 3 times, each time was approximately the same level of difficulty.
Your math stinks if you had trouble mathematically

Coming from someone who used to have the 'teacher' icon and who talks about systems of equations, you sound an awful lot like a math teacher/professor. I'd think almost everyone's math compared to a professional's would 'stink' comparatively. Am I correct, though, math teacher?

Hmm... maybe. But, with the single clue to treat each die as a variable, I'd expect any of my 11th grade students in pre-calculus to be able to solve this with no problem.

 

[bobsmith1492]

Ah, so you're NOT a math teacher...

 

[jagec]

Wow, that's stupid

 

[DrPizza]

Just decided to add this problem to the pre-calculus final exam (as a bonus extra credit problem at the end)
First time I've ever put an extra credit problem on a final exam, but no one's ever gotten all 400 out of 400 points, so it shouldn't be a problem.

 

[jagec]

Originally posted by: DrPizza
Just decided to add this problem to the pre-calculus final exam (as a bonus extra credit problem at the end)
First time I've ever put an extra credit problem on a final exam, but no one's ever gotten all 400 out of 400 points, so it shouldn't be a problem.

boo, it's not even a math question really

 

[AbsolutDealage]

Originally posted by: DrPizza
A=1, B=2, C=3, D=4, E=5, F=6

First roll: 1,1,1,1,1 Total =0. Obviously, 1's are worth 0.
2nd roll: 3,2,6,2,4 2B + C + D + F = 2
3rd roll: 1,5,6,5,6 A + 2E + 2F = 8, but A=0 So, 2D + 2E = 8
4th roll: 3,1,3,1,1 3A + 2C = 4. Since A = 0, then, C =2.

Going back to 2nd roll, B, D, F = 0
Going back to 3rd roll, E = 4
Done.
A, B, D, F = 0
C = 2
E = 4.

Then, I said "ohhhh, I get it... that was stupid."

I ran the game 3 times, each time was approximately the same level of difficulty.
Your math stinks if you had trouble mathematically

This is how I ended up doing it as well. I guess I just wasn't able to see the pattern right off like some of the others in here.

It still bothers me that a professor couldn't have done this math... this could be a decent math problem for 2nd semester algebra.

 

[AsiLuc]

Dear DrPizza, what if the problem was of such nature that it can't be solved they way you're trying?
And isn't it clear that common sense works better here? Just try to understand the question? Dumb people are conspicuously smart to me!

 

[DnetMHZ]

That was pretty easy.. got it in about 1 minute

 

[Smilin]

It kicked my butt.

Problem is I got into this solution early:
Take the number of Odd dice rolled and multiply it by two.

The bitch is it works a large percentage of the time so my mind got stuck trying to figure out some variation that would work.

Finally got it though.

 

[DrPizza]

Originally posted by: AsiLuc
Dear DrPizza, what if the problem was of such nature that it can't be solved they way you're trying?
And isn't it clear that common sense works better here? Just try to understand the question? Dumb people are conspicuously smart to me!

I don't think I'd call the solution to that problem "common sense." IIRC, in the other thread on this problem, many people had trouble getting a solution. It almost seems odd that the average time in this forum is about 1 minute, yet the average time in Off Topic was far greater. Most people (including myself) did not immediately pick up on the meaning of "petals around the rose."

As far as my method not being able to arrive at a solution, well, I suppose that's possible, if my initial thought that each die was worth a specific value was wrong. Fortunately, that initial guess was correct, in which case, a solution would follow. (if there was a solution.) I suppose if the center die was considered the rose, and the other 4 die were considered the petals, then my method wouldn't have worked. (or some other such weird thing.)

My initial guess was to just count the dots on the outside of the dice, eliminating the 1, and counting the 3 as 2 and the 5 as 4. But, I also counted the 6's as 6. I seized upon modeling the problem the way I did because I recognized that if that's how the solution was gained (each die had a value), then my method WOULD have a solution, and it would be extremely easy (for me, since I knew the solutions were integers and I do problems like that frequently)

Incidentally, if it is true that Dr. Duke teaches gaming/simulation courses, and it took him a year to figure it out, then Dr. Duke does not belong in the capacity of teaching those types of courses.

 

[uart]

Dr P, I think you were somewhat lucky to choose a the correct functional form to try and solve first up.

For example I first tried to solve it using a simple linear functional of the five variables. That is, let x1 be the number showing on the first dice, x2 the number showing on the second dice and so on, then try to find a linear functional f(x1,x2,x3,x4,x5) = a*x1+ b*x2 + c*x3 + d*x4 +e*x5 that matches the "petals around the rose". Clearly this approach did not work as the data was inconsistent. When this didn't work for me I started looking for more obscure relations than a simple linear functional, this was my downfall.

Now what you (Dr P) tried was somewhat different, instead of using a linear functional of the raw variables you went for a linear functional of the variable frequencies. That is, let v1 be the number of times a one occurs, v2 the number of times a two occurs etc, then look for a linear functional f(v1,v2,v3,v4,v5,v6) = a*v1 + b*v2 + c*v3 + d*v4 + e*v5 + f*v6. By luck this one worked.

The way I see it, the difficulty with this problem for the intelligent person is that they more fully appreciate the sheer number of functional forms that are possible, and this is daunting. Also they may make less assumptions about the nature of the problem, choosing to only to use the scant information that is definitely known, and so initially describe the problem as no more than a mapping from [1..6]^5 to an unknown range. Even after making numerous trials and determining that the range is probably even integers from zero to twenty, you still end up with an effective range of [0..10] and so a mapping from [1..6]^5 to [0..10].

There are 11^(6^5) unique possibilities for the above mapping! This number is so large that it makes even large cosmological data, like the number of seconds elapsed since the Big-Bang, or the number of atoms in the known Universe, pale in comparison! It is in fact larger than the product of number of atoms in the known Universe times the number of nanoseconds since the Big Band! No wonder I was daunted.





The "Spam in my InBox" Challenge"
Just as an example of some of the types of functionals I was attempting before I finally "saw" the solution I have made up a new challenge. It's called "The Spam in my Inbox" and uses the rolls of 5 dice to uniquely determine the amount of Spam I have. It is a fairly simple relationship that can be described in one sentence and I've made 30 random trials and tabulated the results.

I was going to post it here but decided to make it a seperate thread, so go take the "Spame in the Inbox challenge HERE.

 

[silverpig]

Originally posted by: DrPizza

Originally posted by: lexxmac

Originally posted by: DrPizza

I ran the game 3 times, each time was approximately the same level of difficulty.
Your math stinks if you had trouble mathematically

Coming from someone who used to have the 'teacher' icon and who talks about systems of equations, you sound an awful lot like a math teacher/professor. I'd think almost everyone's math compared to a professional's would 'stink' comparatively. Am I correct, though, math teacher?

Hmm... maybe. But, with the single clue to treat each die as a variable, I'd expect any of my 11th grade students in pre-calculus to be able to solve this with no problem.

You're also assuming that it's a simple linear system. What if the central die was the "rose" and the number of petals was the product of dice 1 and 2 divided by the difference between dice 4 and 5, or the number of dots total divided by the number of dots on the even dice? There are just so many different ways to look at it mathematically

 

[DrPizza]

Originally posted by: silverpig


You're also assuming that it's a simple linear system. What if the central die was the "rose" and the number of petals was the product of dice 1 and 2 divided by the difference between dice 4 and 5, or the number of dots total divided by the number of dots on the even dice? There are just so many different ways to look at it mathematically

I agree... I went with K.I.S.S, and decided that would be the simplest solution.
UART is kicking my butt with the new challenge... I stared at it for 20 minutes during lunch.
(don't you hate it when you see a solution that works for about half of them, then you spend forever trying to adapt that incorrect solution to account for the rest of them?)
If I didn't have to make copies of a calc-final, I'd continue staring.

edit: incidentally, I discounted any division in the problem due to the solutions being integers. Plus, once you get to rounding, you've made it far more complicated a solution than children would be able to figure out.

 

[Jeff7]

Originally posted by: Smilin
It kicked my butt.

Problem is I got into this solution early:
Take the number of Odd dice rolled and multiply it by two.

The bitch is it works a large percentage of the time so my mind got stuck trying to figure out some variation that would work.

Finally got it though.

After a few minutes of rolling and guessing, I figured I'd try the "redefine the problem" - and try to figure out what rose they were talking about. After finally getting that, it never occurred to me that there was a simpler way of doing it. I'd look for anything with a central dot, and "petals" or dots, around it. Add the number of dots that are petals. Never noticed that they were all odd. Duuuhhh...
Weird game.

 

[nlmodel]

yeah i did it the same way u did the first time..i mean read the title...pedals and roses..u see any roses? but what would a rose look like if it were a die? how about a central dot with Petals? lol this was retarded and easy at the same time..soemtimes the simplest solution is the best solution

 

[gordanfreeman]

somehow i doubt i would have ever gotten it w/out starting to read through some of the responses. and all the attempts at solutions using math just made me more confused

lol i havent taken a math course for 2-3 years now (since junior year HS) and never will have to again the direction my education is taking me now. all that stuff makes no sense to me anymore :frown:

 

[FiberoN]

 

[Chu]

Originally posted by: beansbaxter
Anyone seen this and tried it? How long did it take for ya to figure out?

Petals Around the Rose

I had some trouble with it, until I saw the quote in the article 'The Smarter You Are - The Longer It Takes To Figure Out.' Took 1 try after. Weird.

 

[FiberoN]

Can't get it....rofl...:|

 

[Topher]

No luck for me, but it's late and I'm getting tired. I'm making it way harder than it needs to be obviously....

 

[OdiN]

Hrm...well I didn't see the thread in OT and didn't read beyond the first post here before trying my luck. I got it solved within like 10 seconds.

I don't think that if you get it quickly you are not smart or capable of finding a mathematical solution to the problem. It's just a different way of thinking of things. Basically the title of the test gives away the answer. I just thought about that for a few, gave it a shot and it worked. It makes sense on both mathematical levels and basic reasoning. Either way I didn't find it to be that hard of a puzzle. How true the teacher's statement about being smart causing you to take longer. I can understand this because too often I try to find more complex solutions to problems that have simple answers. That is my downfall in math - I always wanted to see beyond what existed. I even would do geometry problems some long drawn out way and get the correct answer...however if applied to a similar problem with different numbers, etc. it would not work. But I would somehow pull out a way to solve a problem specific to that problem. It's really strange.

*EDIT* I'm stopping myself now before I start to ramble on in a philosophical manner

 

[Apologiliac]

I think the way the test was meant to happen was that the person answering the problem would first go through all sorts of things mathmatically and finally take a step back and look at the overall picture,while another person who seees things in a simpler light wouldnt think to do math right off the bat and only see the visual answer. Hence doing math would take longer making you 'smarter' by the tests standards.

 

[OdiN]

Originally posted by: Apologiliac
I think the way the test was meant to happen was that the person answering the problem would first go through all sorts of things mathmatically and finally take a step back and look at the overall picture,while another person who seees things in a simpler light wouldnt think to do math right off the bat and only see the visual answer. Hence doing math would take longer making you 'smarter' by the tests standards.

I can take all day to dig a 50-foot hole by doing backbreaking manual labor, or I can rent a tractor and do it in a few hours. Just because you take longer to do something, doesn't make you smarter. In fact, truly you would be smarter to do something in the most efficient manner possible, all other things being equal. I realize that renting a tractor may cost money whereas digging a hole yourself doesn't (disregarding the fact that it takes up more of your time which arguably can have a monetary value).

Basically, one person's "smart" is not some other person's "smart." It's all subjective really. Personally I do not prefer the title smart, but rather prefer to think of myself as intelligent.

Who's to say for certain what makes one person inherently smarter than another? True it goes both ways. Solving the issue faster doesn't make you any smarter than taking longer to solve the issue, so the teacher's statement is pretty much irrelevant. Also, it is probably being taken out of context somewhat.

Hrm....well I stopped myself last time but couldn't this time

 

[Macro2]

I do agree that the smarter you are mathematically the harder it is to get the answer.

 

[OdiN]

Originally posted by: Macro2
I do agree that the smarter you are mathematically the harder it is to get the answer.

I think that's a ridiculous assumption. Define harder. Because something takes longer to do than something else, does that mean it is harder or easier? Is it not possible to be mathematically inclined, but also see the true answer of something in a non-mathematical way? Would it be possible to solve a non-mathematical problem mathematically? And does that make you "smarter" if you solve it mathematically? Why? If "smarter" is an inability to comprehend something at multiple levels, then do you want to be smart?