A seemingly intractable problem

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A seemingly intractable problem

Postby Scruffy Nerf Herder on December 13th, 2016, 7:35 pm 

Can you solve and explain this problem? I've had enormous fun thinking about it, but I've yet to finally deduce the values of the symbols, and would like to see if someone can puzzle out every inference required to arrive at the conclusion.

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Re: A seemingly intractable problem

Postby Dave_Oblad on December 14th, 2016, 8:09 am 

Good one Scruffy,

I'll have a crack at it when I have more time.. I have to go to bed now. I Like these.

Regards,
Dave :^)
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Re: A seemingly intractable problem

Postby NoShips on December 15th, 2016, 6:21 am 

Great puzzle, Scruffy! I don't have the answer, but I sense that I might be tanatalizingly close to it. Let's see if someone else can get me over that final hurdle...

First, an examination of the elements, and my shorthand for each:

Red squares: I'll call them resques
Green circles: grircles
Pale triangle: priangle
Purple rhombuses: pombuses

Each element comes in its basic form, as well as in a 2nd-level and 3rd-level form (as represented by larger size), with the conspicuous exception of the resques which, perhaps conincidentally, only appear in their basic form.

I suggest we forget all about substituting symbols for simple numbers and mathematical operators: you've probably all tried what I tried -- to no avail! I suspect nothing but the most basic arithmetic is involved, no pen and paper necessary, and the solution will be orgasmically instananeous -- just as soon as we hit on the damn key!

What I suspect is the key to whole puzzle is a game (perhaps a card game or board game), or a sport, or some other activity, which has a 3-level hierarchy, but non-linear method of scoring (like tennis, for example, that goes up from zero to 15 to 30 to 40, and so on, in an indirectly additive manner).

Consider Monopoly. It has the requisite 3-level hierarchy we need -- undeveloped property, property with houses, and property with a hotel -- but clearly doesn't fit the conceptual scheme before us.

Consider playing a game where, at the end of a particular hand or board, we have to add up our respective scores. Taking the third line of the puzzle as our paradigm, Scruffy might announce, for example, "I have a double (which doesn't necessarily imply literal doubleness: -- call it 2nd-order, level 2, silver, etc) priangle with a single pombus, a triple priangle with a single pombus and a single resque, and a single resque."

Dave, meanwhile, calls out, "You score the same as me. I have a triple priangle with a single pombus and a single priangle, a double priangle with a single resque, and a single grircle".

All we have to do now is think of the activity that fits the paradigm, and Bob's your uncle.

Then again, I could be hopelessly off base :-)
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Re: A seemingly intractable problem

Postby NoShips on December 15th, 2016, 7:00 am 

Brainstorming time... What do the 29, 23, and 18, respectively, in the first three equations refer to?

Just plain old numbers? I kinda doubt it. Points? Pounds? Days? Dollars? Temperature? Age? Number of boxes that we have to think outside?

Why are there only four elements? Chance? (Could be *shrugs*). What things come in fours? Card suits? Um, seasons? Stephen Seagal assailants. Bridge players...


Epilogue:
----------

"Well, what have you got, NoShips?"

"Pretty pathetic really. I've got one grircle, four resques, and a priangle, making a grand total of eighteen."

"That's doing it the hard way, dude".

"Tell me about it".
Last edited by NoShips on December 15th, 2016, 8:58 am, edited 1 time in total.
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Re: A seemingly intractable problem

Postby NoShips on December 15th, 2016, 8:16 am 

Damn, this is maddening. I don't mind a few sleepless nights if one can go down in legend and song at the end of it all. The prob is with puzzles like these, one is never quite sure if the effort is worth it. For example, when a trusted friend says, "Don't give up. It's a good one!!" we slug on heroically.

Um, where'd you get this, Scruffy? (after all, don't have that many neurons to spare these days)



In the meantime, try this one:

7111 = 0
8809 = 6
2172 = 0
6666 = 4
1111 = 0
2222 = 0
7662 = 2
9313 = 1
0000 = 4
5555 = 0
8193 = 3
8096 = 5
4398 = 3
9475 =1
9038 = 4
3148 = 2


2889 = ?

If you can't get it, ask the kids:-)

(There's an easy way and a hard way. Von Neumann would do it the hard way -- and still get it in three seconds. Sigh)
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Re: A seemingly intractable problem

Postby Braininvat on December 15th, 2016, 11:33 am 

5

got it in 20 seconds

Haven't started on the OP, but the shapes seem to be types of operation?
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Re: A seemingly intractable problem

Postby NoShips on December 15th, 2016, 11:34 am 

You mean his or mine? LOL

Mine is right.
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Re: A seemingly intractable problem

Postby NoShips on December 15th, 2016, 11:36 am 

Yeah, just count the loops. I did it the Von Neumann way (:-
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Re: A seemingly intractable problem

Postby Scruffy Nerf Herder on December 15th, 2016, 3:20 pm 

NoShips » December 15th, 2016, 5:16 am wrote:Um, where'd you get this, Scruffy? (after all, don't have that many neurons to spare these days)


I got it from here*.


Mod note [2016 12 17 1819, Natural ChemE]: This is not a real IQ test. Content may be grossly misleading.
Last edited by Natural ChemE on December 17th, 2016, 7:20 pm, edited 1 time in total.
Reason: Added disclaimer.
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Re: A seemingly intractable problem

Postby Braininvat on December 15th, 2016, 4:58 pm 

Possibly the 2nd and 5th equations are a wedge in the door.
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Re: A seemingly intractable problem

Postby NoShips on December 16th, 2016, 5:13 pm 

Well, two days of struggling got me nowhere. Still can't get it. Obviously not in the top 1%.

Far more importantly, you've no idea how far a kind word goes at times like these.

Thank you, Paul.
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Re: A seemingly intractable problem

Postby Braininvat on December 16th, 2016, 6:10 pm 

Shapes come in 3 sizes. Could be orders of magnitude. Put a shape inside another, indicates division. Say diamonds are 10, 100, 1000. Then equation 2 becomes true: "100 ÷ 10 = 10"

Could be dead wrong, but that's my starting point.
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Re: A seemingly intractable problem

Postby vivian maxine on December 16th, 2016, 6:14 pm 

Braininvat » December 16th, 2016, 5:10 pm wrote:Shapes come in 3 sizes. Could be orders of magnitude. Put a shape inside another, indicates division. Say diamonds are 10, 100, 1000. Then equation 2 becomes true: "100 ÷ 10 = 10"

Could be dead wrong, but that's my starting point.


Is the answer really five? I thought it was 8. :-)
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Re: A seemingly intractable problem

Postby NoShips on December 16th, 2016, 9:50 pm 

I've tried everything within my 99% hoi polloi powers. Even ironing and shivering.

Um, stick yer 1% up yer elitist hooter, guvnor.

I mean, got any easier questions, or a back door?
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Re: A seemingly intractable problem

Postby Positor on December 16th, 2016, 11:59 pm 

Braininvat » December 16th, 2016, 10:10 pm wrote:Shapes come in 3 sizes. Could be orders of magnitude. Put a shape inside another, indicates division. Say diamonds are 10, 100, 1000. Then equation 2 becomes true: "100 ÷ 10 = 10"

On the other hand, the size of a shape seems to correlate to the space needed to fit other shapes into it, so it may not have any intrinsic significance.

Here are some initial assumptions I have been making (without any success so far):

Shapes side by side = addition
One shape within another = multiplication
All values are whole numbers (likely, since all the given numbers are whole)
Diamond = 1 (giving 1 x 1 = 1)
Triangle = a negative number (hence squaring it gives a positive value). This introduces some (perhaps large) minuses into the equations, which gives more possible values to play with.
Square and circle = either positive or negative numbers, but at least one of them must be positive (to make the fifth equation add up to +18)

However, I may be completely wrong!
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 12:23 am 

My advice is exhume Einstein, so that we all might get a good night's sleep.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 4:25 am 

Does anybody want a clue?
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 4:39 am 

No, I'd rather just live a life of servitude. Need any doughnuts, massa?

Seriously, did you figure it out. Lomax?
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 4:39 am 

NoShips » December 17th, 2016, 9:39 am wrote:No, I'd rather just live a life of servitude. Need any doughnuts, massa?

Seriously, did you figure it out. Lomax?

I spent all night on it. I can't resist stuff like this.
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 4:42 am 

Clever lad. I'd love to hear, but the website Scruffy directed us to requests that we don't make these things public (lest morons like me gain power and knowledge).

Send me the answer in PM, please. Erm , and what can I do for you?
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Re: A seemingly intractable problem

Postby Dave_Oblad on December 17th, 2016, 8:34 am 

Hi all,
I haven't had a chance yet to spend much time on this..

So Far:

The system must be Mathematical to produce (29,23,18) solutions.
The system must be base 10 or higher to have a 9 as Least Significant Digit in 29.
It could be presumed the gap between symbols indicates Addition as Multiplication could grow too fast in some sequences.

(Top Center)
It wouldn't be fair to have two distinctly different symbols represent the same value.
Thus (top-center) (Large Blue Diamond) must indicate Squared or Division of contents.
But Division could lead to fractions.. and I doubt that's allowed (but not eliminated yet).
Thus (Small Blue Diamond) must be zero or one, as in 1x1=1 or 0x0=0.
If (Large Blue Diamond) is multiply contents by a constant (2,3,4 etc) then (Small Blue Diamond) can only be a zero.

Some large outside symbols could represent Multiply contents by -1. If this is true for (Large Blue Diamond) then (Small Blue Diamond) can only be a 0.

(solution that equals 18)
The (Small Red Squares) can only be 0 or 1 or 2 or 3 or 4, If 4 then the sum of 4 (Small Red Squares) would be equal to 16 leaving a remainder of 2. Thus, of the two remaining symbols, they would have to be 0 and 2 or 2 and 0 (Small Green Circle) or (Small Yellow Diamond).
(Small Green Circle) or (Small Yellow Diamond) must both be Even, or both be Odd, numbers to produce an Even 18 value.. given 4 (Small Red Squares) can only be an Even value as 0,4,8,12 or 16.

That's as far as I've gotten.. given the last 15 minutes of working on the problem. It's bedtime for me and tomorrow I have company for most of the day, so I hope no one posts the solution until I have a chance to dig in further.

As is the case in many of these, I may be over thinking the solution.

So a hint Lomax..

Am I over thinking the solution?

If Not over thinking, is my reasoning above sound so far?

Regards,
Dave :^)
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 12:16 pm 

Dave_Oblad » December 17th, 2016, 1:34 pm wrote:(Top Center)
It wouldn't be fair to have two distinctly different symbols represent the same value.
Thus (top-center) (Large Blue Diamond) must indicate Squared or Division of contents.
But Division could lead to fractions.. and I doubt that's allowed (but not eliminated yet).
Thus (Small Blue Diamond) must be zero or one, as in 1x1=1 or 0x0=0.
If (Large Blue Diamond) is multiply contents by a constant (2,3,4 etc) then (Small Blue Diamond) can only be a zero.

Some large outside symbols could represent Multiply contents by -1. If this is true for (Large Blue Diamond) then (Small Blue Diamond) can only be a 0.

Okay, here's your hint: they didn't make it fair. The big outside symbols are a red herring - large diamond means something different to small diamond, and something different to large triangle. You're right that they represent functions of the inside shape though.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 6:22 pm 

Wish you hadn't introduced me to this test, Scruffy. It's going to be a long time before I get anything done.
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Re: A seemingly intractable problem

Postby Natural ChemE on December 17th, 2016, 7:16 pm 

Folks,

Just wanted to warn that the thought that went into that alleged IQ quiz is really warped, and its creators appear to have been emotionally/mentally unbalanced.

Solving questions is always fun, though I'd strongly suggest no one take that alleged IQ test as anything more than a collection of silliness. There's this weird, sickly air about it.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:23 pm 

Natural ChemE » December 18th, 2016, 12:16 am wrote:Folks,

Just wanted to warn that the thought that went into that alleged IQ quiz is really warped, and its creators appear to have been emotionally/mentally unbalanced.

Solving questions is always fun, though I'd strongly suggest no one take that alleged IQ test as anything more than a collection of silliness. There's this weird, sickly air about it.

I'm curious ChemE. Are you basing this on the nature of the quiz (for instance, the fact that question 6 is underdetermined) or is there something you know about its creators?

I won't go mad, but I will let these questions bug me. Q4 is forcing me to rediscover mathematical methods I'd forgotten.
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 7:24 pm 

Lomax, you're wonderful. Well done, sir.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:30 pm 

NoShips » December 18th, 2016, 12:24 am wrote:Lomax, you're wonderful. Well done, sir.

Did you get the answer to Q2?
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Re: A seemingly intractable problem

Postby NoShips on December 17th, 2016, 7:31 pm 

Erm, I've been a little preoccupied, L. Almost went mad over these dang triangles. LOL.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:35 pm 

NoShips » December 18th, 2016, 12:31 am wrote:Erm, I've been a little preoccupied, L. Almost went mad over these dang triangles. LOL.

Haha. Well I'll let you in on another reason why the quiz is cruel: Q2 is underdetermined too, as far as I can tell. It's not possible to just simplify the equations given what you (reasonably) know, and then solve them together. I had to try a few ex hypothesi possible values for the shapes in equation five, and plug them into equation 1 to see if they worked. Which meant making assumptions about what the big triangle might mean, too. So there's guesswork at all steps. But the answer - when you get it - kind of seems simple and beautiful enough that you figure it must be the one they were after.
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Re: A seemingly intractable problem

Postby Lomax on December 17th, 2016, 7:35 pm 

(And once again, we owe our thinking to Quine.)
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