What is the name of this operation? (Inverse Exponent?)

[Algr]

So this puzzle has been wandering the internet. I find it unsolvable because there is no way to determine what operation is being performed to the double fries. Everyone assumes it is addition, but addition and multiplication are performed with signs elsewhere in the puzzle. If we assume that the two fries are being multiplied, then the value of a singe fry is √2.

But what if the double fry is exponention? What is the inverse operation called?

MathPapa doesn't know how to solve X^X=2. I was able to just keep typing guesses in until I got an answer of exactly 1.5596105, but I doubt that this is correct because it is rational.

 

[mfb]

1.5596105^1.5596105 is approximately 2.000000088219.

There is no "good" way to solve this analytically. You can write down a solution using the Lambert W function but the definition of the function is basically "let it be the solution to this problem" (not exactly, but that is the idea).

 

[mjc123]

Maybe I'm being dense, but what is the puzzle? It looks like drink = 10, burger = 5, double fries = 2, ? = 60 or 15 depending on whether you work sequentially or by BODMAS.

 

[Algr]

Lots of people get wrong answers from failing to notice that the fries are doubled, or that the last operation isn't addition, or from forgetting PEMDAS.

 

[jedishrfu]

So shakes are 10 and burgers are 5 and fries are 1 from the first three lines

So the answer to the last one is shake + fries * burger = 10 + 1 * 5 = 15

There’s no magic here just some observations of double fries and the times in the last and how to apply it.

 

[Algr]

X⋅X=2 ; X=√2
X^X=2 ; X=?2

Really? No name for this operation? Given how important exponents and square roots are, I'm surprised that this doesn't turn up more. I recall someone came up with a process for systemizing the math operations, such that +=1, x=2, -=-1 and so on. So this operation would be -3? Google isn't helping me find this. Does anyone recognize what I am talking about?

Mfb; Thanks for the link. It's a bit above my knowledge, but I am working on it.

 

[jbriggs444]

X⋅X=2 ; X=√2
X^X=2 ; X=?2

Really? No name for this operation? Given how important exponents and square roots are, I'm surprised that this doesn't turn up more. I recall someone came up with a process for systemizing the math operations, such that +=1, x=2, -=-1 and so on. So this operation would be -3? Google isn't helping me find this. Does anyone recognize what I am talking about?

https://en.wikipedia.org/wiki/Tetration#Square_super-root

 

[Mark44]

So this puzzle has been wandering the internet. I find it unsolvable because there is no way to determine what operation is being performed to the double fries. Everyone assumes it is addition, but addition and multiplication are performed with signs elsewhere in the puzzle.

It's certainly inconsistent, but I think that it's reasonable to assume that the double fries image means two fries. Keep in mind that we can write 10 as either 2 * 5 or 5 + 5. Likewise, we can add one hamburger to another to get two hamburgers, or multiply one fry by 2 to get two fries. Interpreting the double fries image as meaning "fry times fry" doesn't make any sense.

If we assume that the two fries are being multiplied, then the value of a singe fry is √2.

The principle of Ockham's Razor comes to mind; "If there are two explanations from some event, choose the simpler explanation."

If you do a web search for "MacDonalds math puzzle" you get lots of hits, such as this one: https://www.today.com/food/mcdonald-s-style-math-brainteaser-stumps-internet-t107484
The writer for this one comes up with an answer of 15, which is what you would get if you realize that 5 + 1 X 10 equals 15, using the standard rules for evaluating arithmetic expressions.

 

[Algr]

https://en.wikipedia.org/wiki/Tetration#Square_super-root

Ah ha! This is what I have been looking for! Thank you! It also leads to Hyperoperation, which is the answer to my other question.

Mark44; I agree that addition was probably the original author's intent, but frankly it isn't conveyed clearly, so I think it's fair to point out the other possible interpretations.

 

[Mark44]

I agree that addition was probably the original author's intent, but frankly it isn't conveyed clearly, so I think it's fair to point out the other possible interpretations.

I disagree, based on what I said about doubling something by either addition or multiplication by 2. As I said already, you can one fry to another or you can multiply a fry by 2, and get two fries in both cases, but multplying one fry by another makes no phsical sense whatsoever.

 

[Algr]

Sure it does. The foodstuffs are like variables. If you put two variables together like this: XY=0 . It means multiplication. (So at least one of those variables is 0.) And since one of the fries is higher then the other, it also resembles X^Y. But the most important thing to remember is that this visual is for the kinds of forums where no one ever convinces anyone else of anything.

 

[Mark44]

Sure it does. The foodstuffs are like variables. If you put two variables together like this: XY=0 . It means multiplication. (So at least one of those variables is 0.)

This makes no sense at all. My explanation of adding two food items or multiplying a food item by a positive number makes sense whether we're talking about food items or numbers.

Your example makes no sense if we're talking about food items. You can't multiply a hamburger by a hamburger. Period.

And since one of the fries is higher then the other, it also resembles X^Y.

That' makes even less sense. I would be willing to bet that the designer of the puzzle never dreamed that someone would interpret two packets of fries as $\text{fry}^{\text{fry}}$.

This thread has veered off into the ridiculous long enough, and is now closed.