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Math riddle


USNRET

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22 hours ago, DrWho said:

I'm not sure I'm tracking with you Jeff.

 

Just think through the mathematical grammar of the riddle....

 

It starts with 1 + 4 = 5. Okay, that's easy for everyone to understand.

The next line starts with 2 + 5 = 12. Okay, normally we expect 7 in a Base 10 system. The riddle doesn't have 7 as the result, so now the logical process is to reevaluate our assumptions. Perhaps it's not a Base 10 system? A quick check reveals that a Base 6 system gets the closest, but 2 + 5 = 11 in Base 6, not 12.

 

Okay, so maybe the numerical symbols have different weighting? At this point I would pause and point out that this is really digging deep into "assumptions" and there isn't much value in changing the weighting of numerical symbols. However, it is a riddle and we must at least assume proper grammar, right? Isn't grammar usually at the foundation of most riddles? Unfortunately the symbol for 2 exists in both sides of the equation, which poses certain limitations on how addition works. To end up with the same least significant digit, you must add by an integer count of the Base....Base 5 doesn't have a digit for 5 (five is represented by 10 in base 5). If you understand how to count, then this should be an aha moment at the absurdity of what was written.

 

I could expand on more problems with the riddle (I actually analyzed several others before seeing the fundamental counting problem), but I don't think it's valuable to delve deeper because the problem statement itself is clearly broken. I used spelling as a visual example, but this is really deeper than spelling. It's striking at the very fundamentals of math. I get on a bit of a soap box when it comes to math because these simple fundamentals are actually wrought with incredibly deep truths....and our educational system totally misses it - at all levels of education. I also have a huge vendetta against this "infotainment" crap that propagates social media. It's not that I'm against information being entertaining, but it should never be at the expense of truth. The laziness that goes into these little quips really erodes away at the knowledge of our culture - but it often goes by ignored because of the satisfaction we feel for "seeing it". I'm not just talking math riddles, but all the other reductionist simplification of incredibly complex interactions. My Facebook wall is full of "friends" posting these prideful, yet ignorant remedies.

 

Back to this riddle, you only "see it" when you don't submit to a proper understanding of counting and addition....and yes, it's really that bloody fundamental. The crazy thing is it wasn't until well after college that I realized I hadn't learned how to count properly. Not that I couldn't count, but I didn't fundamentally understand it to the level I do now....and it's that new understanding that makes this riddle incredibly annoying. I think we way underemphasize the wisdom of the ancients that were exploring the depths of mathematics. 

 

 

In other words, I agree with Quiet Hollow who said it in much fewer words :)

 

 

 

You're annoyed because you assumed this is a math problem and went off into the weeds looking at different numbering systems etc. When things don't make sense using conventional thinking, you conclude that it's useless gibberish and dismiss it.  

 

Anyone can do math.  This, however, is simply an example of cryptography and it's intentionally misleading. You're given a set of conditions that provide a key to a code and then asked to decode a new expression to determine the encrypted value.  Several people got it right off the bat.  In this example of "a+b=?", in order for the expressions to work according to the given conditions, "+" does not mean addition.  There is a simple function applied to the sets of ordered pairs of numbers represented by the "+" symbol where "+"=fn(a,b)=ab+a.  Applying that function to the ordered pairs is the only universal way to arrive at the answers given for the stated conditions of the key. Using that function, you can decode any similarly structured expression without relying on a series or whole numbers only differing by three.  

 

If I wanted to tell someone who knew the code that there are 50 silos in a missile squadron, using the encryption, I'd say there are 5+9 silos and an eavesdropper would underestimate the squadron missile strength at only 14.

 

added:  I don't want to come off sounding like I'm challenging anyone's genius credentials but it is interesting to see how people think - much like the ol "plane on a conveyor" thread a few years back.

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10 hours ago, sputnik said:

You're annoyed because you assumed this is a math problem and went off into the weeds looking at different numbering systems etc. When things don't make sense using conventional thinking, you conclude that it's useless gibberish and dismiss it.

For what it's worth, I actually saw the patterns quite readily. The reason for my comments is because I've realized that I need to practice submitting to "conventional thinking" in order to be a successful engineer. Math just works - there's a reason it exists. Anyone can find patterns. Not everyone can determine causality. Understanding the causality is where I think the genius resides because that's how one then controls the mechanism and actually does something with it.

 

I do find it interesting though that you immediately went to a different notation to describe redefining the function indicated by the + symbol. However, if you're going to redefine the + symbol to mean another function, then why are you using the + symbol to denote the 'new meaning' and 'classic addition' at the same time? Yes, I understand colloquially what you're trying to communicate, but it's still not logically presented. Using substitution, your function requires that fn(a,b) = fn(ab,a). The solution space for that function definition does not include the numbers presented in the riddle:

fn(1,4) = 1x4 + 1 = 5.

fn(1x4,1) = 1x4x1 + 1x4 = 8.

 

If you want to redefine the + symbol to denote a function that satisfies the number set of the riddle, then you must also create a new symbol to denote classic addition.

 

Yes, I'm totally being obtuse, but it's with the intent of denoting the beauty of the math as the language of logic. Why not just present the riddle as follows:

fn(1,4) = 5

fn(2,5) = 12

fn(3,6) = 21

fn(8,11) = ?

 

This way we don't have to play games with semantics, and we can honor the beauty of math in the process. We can then also apply linear algebra to this given set to derive the possible outcomes for the question. If we allow for any dimensionalality in the function, then there is a going to be a confined infinite number of answers. The fn(a,b) = ab+b is not the only solution space. We could have any of the 3rd order and above polynomial expressions, or we could implement a recursive function.

 

A true genius would derive the form for the entire solution set. That is what the field of linear algebra explores. I think the solution set in this case might actually be unconfined infinite, so why not throw in any result for fn(8,11)? I bet we can find a polynomial that satisfies all numbers between 0 and infinity. But if that's true, then is it really a riddle? Certainly not a good one! Btw, this result is still true if you want to accept redefining the + symbol to be an arbitrary function....and that's my point, it's a totally ignorant riddle in that regard. And that's why an answer of 19 makes way more sense....and the riddle is that two of the statements are false, which would even fall into your cryptography argument. Obfuscation is a very good tool for hiding meaning.

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19 hours ago, Jeff Matthews said:

Who, you're just trying to be above what is a socially-accepted norm of testing problem-solving.  I guess geniuses like you get annoyed with them, but most of us morons just solve the problem.

I didn't see this post until just now.....I think my posts are getting interpreted as some arrogant prick trying to piss in your cereal....which is totally not the intent.

 

I am always on a constant pursuit of improving my understanding of the world. I saw this riddle and was thinking oh cool, this will be fun. I figured out a solution, then read the posts from others before replying, and then realized there were multiple ways of analyzing it. Then I took a step back to see if there was a way to determine which of the offered solutions was more valid. It was then that I realized the whole thing is illogical. When illogical crap is presented as "only worthy of genius" (as implied by the riddle itself), then I think it certainly warrants telling the emperor he's not wearing any clothes. Not once was I thinking "check out this intellectual flexing". Unfortunately it is very difficult - especially in written form - to accurately depict the offness of the riddle. I think I probably burned close to 4 hours trying to understand these ideas well enough before I could start putting words together.

 

But if that's how it came across, then I'm sorry for pissing in your cereal. Honestly, I just wanted someone to share in the aha moment.

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