A really unfortunate math problem

[Flipi]

Hi eveyone, i'm completely new to this forum and i would like to ask you a question. So i randomly saw this "problem" on my facebook feed:

So i tought... well le'ts try to solve it... so i got 21.4142. but there was nobody else that got this answer and i was shocked... so i checked my math a few more times and it was right... now i understand why someone would say 21 (logically speaking) but the way that i understood this was that it was a mathematical problem (it was even advertised as such)... So i posted the solution with all my math and reasoning behind it (on 9gag.com... yeah i know not the best place to have a mathematical debate) and everyone keeps saying it's wrong and that i'm dumb (like 80 comments of statements like that)... but i still don't understand what's wrong about it... can you help me out and tell me where my math fails.

so this is how i got to my solution. I transformed everything to a purely mathematical formula and found out there are two possilbe solutions.
Let's start with SOLUTION ONE:

we transform horse to x, boot to z and horseshoe to y (just to make it easyer to write) and it goes like this:

the first one:

x + x + x = 30
3x = 30
x = 10

the secound one is:

x + y*y + y*y = 18
y*y + y*y = 8
2y*y=8
y*y=8/2
y=square root of 4
y= 2

(btw i used multiplication because there is no mathematical symbol between the horseshoes. if you think this assumption is wrong in any way go to solution 2)

the third one:

y*y - z*z = 2
4 - z*z = 2
z*z = 2
z = 1.4142 (and so on)

so the solution is:
1.4142 + 10 * 2 = 21.4142

Solution 2:


So we make horse x again, we make horseshoe y and the boot z. But this time we assume that the double variables are completely different so we make double horseshoes a and double boots b (which you mathematically can not prove have any corelation with variables y and z in any other way than from solution 1)

so we start:

x + x + x = 30
x=10

next:

x + a + a = 18
10 + a + a = 18
2a = 8
a = 4

next:

a - b = 2
4 - b = 2
b = 2

so now we try to solve the last one:

z + x * y = d (let's say d is the answer)
z + 10 * y = d (since the only variable we know is x we cannot do much here...)

so basically conventional math can't solve it without additional information on variables.


So to sum it all up... using "simple logic" you can slove the problem (which is no longer a mathematical problem but a logical one) and say it's 21... (asuming that the variable one horse shoe is 2 and the variable one boot is 1 from looking logically at the pictures).
But if you actually start solving it mathematically you can only get two answers... one is 21.4142, and the other one is that the problem is not solvable by our conventional math.

Now since i got attacked by commenters who said i'm stupid and that i'm wrong, i'm really hoping someone can tell me where i went wrong.

Best regards,
Flipi

 

[lookagain]

You left out the most natural (likely) solution:

Solution 3:

horse + horse + horse = 30

horse + 2 horseshoes + 2 horseshoes = 18

2 horseshoes - 2 boots = 2

boot + horse*horseshoe = ?

___________________________________


Translate the above to these equations:

x + x + x = 30
x + 2y + 2y = 18
2y - 2z = 2

z + x*y = ?

 

[Flipi]

Yes like i said, that's the logical solution for most people, but from purely mathematical standpoint that should be wrong because there's no plus between the two boots or the two horseshoes and thus you multiply them like they were any other variable... right? i mean you are using them as a variable, why not treat them like a variable?

P.s. i know i'm probably overcomplicating it, but that's just me

 

[Flipi]

Well, direct your complaints to Facebook

haha yes that should work well i'm not complaining... was just looking for confirmation

 

[mmm4444bot]

Reworded because I had used a symbol that was already in use for something else.

from purely mathematical standpoint that should be wrong

Except that the problem statement has not been presented in a purely mathematical form, so it's open to interpretation.

there's no plus between the two boots or the two horseshoes ... you are using them as a variable, why not treat them like a variable??

Not all objects are variables. Besides, there's no room for any mathematical operator (plus sign or multiplication sign) between the double-looking boots or double-looking horseshoes. In each case, the presentation shows two objects with one overlapping and obscuring the other. (In order for juxtaposition to denote multiplication, you really need two complete symbols next to each other, not one partially on top of the other. A different interpretation would be two objects combined together; that's addition.)

Instead of assigning a new variable, interpret each of the double objects as two times the single object, and then express it in terms of the variable already chosen to represent the corresponding single object.

Because you already assigned the variable y to represent a single horseshoe, it makes sense to assign the expression 2y to represent the double horseshoe (y combined with another y).

Likewise, assign the expression 2z to represent the double boot (z combined with another z) because z already represents a single boot.

i got attacked by commenters who said i'm stupid

That was not called for. :cool:

 

[Flipi]

Except that the problem statement has not been presented in a purely mathematical form, so it's open to interpretation.




The presentation does not show two distinct boots or two distinct horseshoes; in each case, it shows one complete symbol overlapping and obscuring a second. One could interpret each of these new "double-looking" symbols as a new variable, in terms of another.

Like y = 2x. :cool:

for the first statement: it was presented to me as a mathematical problem... (it said can you solve this equation? or something like that)
for the secound statement: What i'm trying to say is, that if you want to treat each symbol as a variable (since you are supposed to find the value of each of them I find it logical to assume that) you can only assume two things, eather each variable (even similar ones) is a variable of it's own and it has no correlation to the other and the equation makes no sense or there are mathematical symbols between them, which would mean you multiply them. What peaople are doing is using them as variables and than not applying the rules of math to it. While i understand the logic behind it (I tought it was 21 too, but then i transformed the pictures into variables x, y and z and the math just didn't add up), I personally belive it's flawed. I'm not trying to start a flame war or anything like that, just wanted to see what other people tought about it when presented with my preception of this problem. And i respect your and everyone elses preception of the problem.

 

[greg1313]

The presentation does not show two distinct boots or two distinct horseshoes; in each case, it shows one complete symbol overlapping
and obscuring a second. One could interpret each of these new "double-looking" symbols as a new variable, in terms of another.

Like y = 2x. :cool:

No, now you're overcomplicating things, mmm444bot. What is presented is a standard way to show more than one thing with a partial
overlay of a picture. Your response defies common sense. No, they are not double-looking" symbols, and they could not be interpreted
as a new variable.

 

[mmm4444bot]

... you're overcomplicating things, mmm444bot. What is presented is a standard way ...

My apologies. I'll try to remember the "standard way". :roll:

But you're correct that using the symbol y as I did was not good. I had forgotten that it was already in use for something else; I have edited my post accordingly.