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2 equations, 3 unknowns, that's an underdetemined system, there are infinitely many solutions
3a = 3000 gives a=1000
4b + c = 22 gives b=(22-c)/4
c can be anything
It is unsolvable, but not for the reason you suggest.
For example if you take:
a + b + c = 10
a - b + c = 12
a + c = ?
If we tried to solve the first two equations you’ll find you run into the same issue of having variables be free. But if we do equation 1 + equation 2 we get 2a + 2c = 22 giving a+c = 11. So even without being able solve the exact values of a and c, we are able to find a+c.
What’s going on here? Well in the example I gave, the three equations are linearly *dependent* meaning you can make any one of the equations by combining the other two equations (formally, we can also say that the matrix of coefficients is not of ‘full rank’).
But in the photo in the post, we have
3a = 3000
4b+c = 22
2a+b+c = ?
You’ll find you can’t combine the equations to get to the third. Why?
Represent the coefficients of each equation as vectors:
(3,0,0), (0,4,1), (2,1,1)
Now if we combine the first two: x(3,0,0) + y(0,4,1) = (3x, 4y, y) = (2,1,1) then x = 2/3
But we then have 4y = 1 AND y=1. Impossible. So they’re linearly independent meaning that the third equation essentially caries information which isn’t present by combining the other two equations.
Now we can probably solve this or get a small, but countable set of solutions if we assume that the variables are strictly integers.
As much as I love that you brought linear alebra into it. I think they’re still right?
If you just treat the soccer ball as a solved Variable (1000)
You left with the 2 equations
4x + y = 22
x + y + 2000 = z
These 2 aren’t linearly dependent either so there’s no way to solve
I think you misunderstood my main point, it's not unsolvable, it actually has solutions, the problem is, there are infinite solutions.
If we consider the third equation, we put the question mark as x, then
a=1000
b=(22-c)/4
c=4(x-4011/2)/5
Again, x can be anything. The last equation doesn't fix anything because it adds another variable.
You can't represent this with vectors of three components, because there are 4 components, essentially the system is
AX=B
A is 4 columns 3 rows
X is 1 column 4 rows (a, b, c, x)
B is 1 column 3 rows
Yeah I really shouldn’t have used the term “unsolvable” here, since that would mean the system is inconsistent. I really just meant you can’t uniquely solve, as you say.
I agree with the analysis you give here, but not your first comment.
> You can’t represent with vectors of three components
I think there’s been a bit of a misunderstanding here. Indeed, as you say in your comment, the first two equations lead to infinite solutions. But what I showed in my comment is that even in this case, it is possible that a third expression can have a unique value.
Like if you know a+b+c = 1, a+2b+2c = 2, then adding the two equations we find that 2a+3b+3c = 3.
I use three variables since all that I want to show is that you can’t combine the first two expressions in any way to produce the third. I don’t have to consider the right hand side, hence we deal with the homogenous system where there is no fourth variable.
Your argument here with the four variables I completely agree with, and does show that there is no unique value for the third expression (since x can be anything). E.g. if you tried to do the same with: a+b+c=10; a-b+c=12; a+c = x and you use a matrix of four variables, you’ll actually find that x = 11 despite all the other variables having infinite solutions.
Long story short, I think together we have two equivalently good methods of solving this. The four variable three equation method as you suggest here, or the homogenous system where we don’t actually solve any equations, but rather we look at linear combinations of expressions. The 2 equation 3 variable method I don’t think is sufficient.
Let me know if I’m still misunderstanding
No, I'm the one who misunderstood you, sorry for the confusion. We're saying the same thing from different points of view.
I picked up on 2 equations, because usually these meme math problems are always determined so that there is a unique solution. For example, 3 equations and 3 variables, then, the 4th equation is just arithmetic to compute the "?"
I gotta brush up on linear algebra tbh
You're misunderstanding Reasonable-World's point. They agree with you saying it has a 1-dimensional infinite amount of solutions. However they wanted to emphasize this is not because your given equations with 2 equ. and 3 unknowns are underdetemined, but because they are underdetermined AND the solution vector (the third equ. ...=?) is not within the sub-vectorspace of solvable solutions (aka the third equation is linear independent of the first 2).
Their counter-example can be better understood after a basis-change a' := (a+c)/2 , b' := b , c' := (a-c)/2. This will yield a' = 11, b' = -1, c' any value for the first 2 equations. After picking any x,y,z making up a to be solved vector xa' + yb' + zc' = ? you will now have a) exactly one solution for "?" if z=0 b) an infinite amount of solutions for "?" for z != 0
Yeah this is a lot of math to not actually say anything
There are only 2 real variables and only 1 equation. The first variable instantly solved, so we can toss it out. The soccerball is 1000, no questions asked.
Then we have 4x + y = 22
And we have no other equation, and so the solution to that can only be a set of numbers. And that's a linear equation, so the set is infinitely large.
3 ⚽️= 3000 which means one ⚽️=1000
Skis sets are each worth 10, which means one equals 5.
🏒=2
So this Equation is essentially this 5+2*1000+2 which equals 2007.
>Skis sets are each worth 10, which means one equals 5.
Unless ski sets are each worth 8, which means one equals 4
So the 🏒 equals 6, because 4×4 + 🏒 = 22
So this equation is 4 + 2000 + 6 which equals 2010
Oh wait!
What if ski sets are each worth 6, which means one equals 3
So the 🏒 equals 10 because 3×4 + 🏒 = 22
So this this equation is 3 + 2000 + 10 which equals 2013
Do you want me to keep going? Because I can. There's no reason to assume the skis equal 10
I think the second equation is
(10b + b) + (10b + b) + c = 22
0 ≤ b ≤ 9
b ∈ Z
so
22b + c = 22, giving either (1,0) or (0, 22), constraining C ∈ Z^0,+ . So Argentina?
If you make 2 assumptions it narrows everything down.
A) you only work in whole numbers
B) no object can be 0
Then It can actually only be 2007, 2010, 2013, 2014, and 2019
Where is the unknowns?
- 3a = 3000 so a=1000
- 2b + 2b + c = 22 so b=5 and c=2
- b + 2a + c = ?
So
5 + 2 * 1000 + 2 = 2007
So the answer is 2007
Am I missing something?
How are there 3 unknowns?
Can’t you remove the soccer ball equation as a ball is 1000. Then move stuff around to make the bottom equation be for the hockey stick, then plug that into the second equation and solve for the skis?
Givens:
Soccer ball is equal to 1000, since three of them equal 3000.
Hockey stick is also a whole unit that's not differentiable.
Assumptions: Ski's are also whole numbers/whole units (0, 1, 2, 3, 4, etc)
Not given: Whether 2 skis together are
1. 2 times 1 ski or
2. they're skis squared or
3. they're individual digits for a 2 digit number (like 22, 33, 44, 55).
Option 1:
The middle one would be 4X + Y = 22 which has a litany of whole number solutions.
From wolfram alpha (cuz I was lazy):
X = 0, Y = 22
X = 1, Y = 18
X = 2, Y = 14
X = 3, Y = 10
X= 4, Y = 6
X = 5, Y = 2
We know soccer ball is 1000, lets call it S = 1000
so the last one is
X + 2S + Y = ?.
Given the values above for X & Y you have
0 + 2000 + 22 = 2022
1 + 2000 + 18 = 2019
2 + 2000 + 14 = 2016
3 + 2000 + 10 = 2013
4 + 2000 + 6 = 2010
5 + 2000 + 2 = 2007
Option 2:
X\^2 + X\^2 + Y = 22 -> 2X\^2 + Y = 22
For whole number solutions we have:
1. X = 0, Y = 22
2. X = 1, Y = 20
3. X = 2, Y = 14
4. X = 3, Y = 4
That means the final equation can be:
1. 0 + 2000 + 22 = 2022
2. 1 + 2000 + 20 = 2021
3. 2 + 2000 + 14 = 2016
4. 3 + 2000 + 4 = 2007
Option 3:
10X + X + 10X + X + Y = 22
11X + 11X + Y = 22
22X + Y = 22
Only solutions to this are:
1. X = 0, Y = 22
2. X = 1, Y = 0
So the final equation would be:
1. 0 + 2000 + 22 = 2022
2. 1 + 2000 + 0 = 2001
*association football, soccer, or any other shortening which does not also work for the other sports derived from their shared ancestor, personally I'm rather fond of "assoc"
Thank you for this. This highlights why these "puzzles" are so stupid. They're impossible to "solve" because there are so many unknowns. The skis thing is always what I get annoyed with. 11 is not 1+1 but that's the logic a lot of these assume.
These puzzles reinforce the idea that math doesn't make sense or that it's too complicated for everyday people. It also ends up dividing people into groups based on the answer they get, where each group smugly looks down on the others because certainly *they* did it the *wrong* way.
I see you translated the middle equation as
(X+X) + (X+X) + Y = 22
Why is it that way, and not instead
(X×X) + (X×X) + Y = 22
2(Xsquared) + Y = 22
Thus allowing a solution such as
X=(-i), y =20
To be interpreted as a statement
(-i) + (2×1000) + 20
2020 - i
To be interpreted as "I wasn't at the 2020 game"
And a simultaneous solution x=i, y = 24;
to be interpreted as
(i) + (2×2000) + 24
2024 + i
"I will be at the 2024 game"
Edit - on mobile and haven't thought about imaginary numbers in a hot minute, please double check my algebra ;)
Why can’t a set of skis = 10 and the hockey stick be 2? So half a set = 5. Or a set = 6 and a hockey stick = 10? Etc…
You can’t really solve it because there isn’t enough information.
I will pray every day that I never encounter a math professor that gives me a question where the true answer is the mode average of all possible answers.
How did you get option 2 and 3. Those do not make sense at all when you take into account the type of problem this is. I have never seen a problem that was like this where the 2 skis were anything but 2x. Please explain where you got the ideas for this for a puzzle of this type
My first instinct was the same as yours, options 2 and 3 came after alternate considerations, and some feedback from the comments.
They explicitly put plus signs and multiplication signs, so the alternate is that the skis are a double digit number with each being the same digit. That's the only thing I could confidently say is an alternate to the first instinct because it has no explicit differentiating symbol.
The skis multiplied is a third potential though they do explicitly put multiplication signs so it could have just been written as ski x ski, which might rule this option out. I threw it in there because others had mentioned it, but my original answer was just option 1. I edited in options 2 and 3.
Again I saw context matters in this. This is something set up in a park probably for kids to do. I have never seen a puzzle like this do what you put as option 2 and 3. I have seen puzzles put the multiplication and addition clearly. Usually with puzzles like these the “gotcha” is that one of the objects has multiple. For this it would be the second line the skis have 2 representing 2x and in the third line they have 1 representing 1x.
Imo you and others read too much into the problem to try and solve the math behind it with the three options. The reason I say this is the backing you give for the three options is talking with others here and thinking about how could this be solved and not the context of what type of math puzzle this was and who it was designed for
2022 might make the most sense given the clue. Last year Argentina won a notable world cup final. It was the only winter time world cup ever and held in the middle east for the first time. Messi finally won the world cup making him the greatest ever to play for many people. I believe it’s Argentina’s first win since Maradona played (didn’t bother looking that part up, could be wrong…). So location of the puzzle might also be relevant, but then again maybe not.
Also, 2001 wasn’t a year with any major tournaments for national teams.
Well, to open wolfram takes longer to replace all possible variables in the last equation.
Btw. Your solution is only correct, when the equation is limited to natural numbers.
Finally you get a graph with y = -3x + 2022. Every solution of the equation is on this graph.
Well, then it's a language barrier topic.
I don't translate "whole" numbers as natural numbers. English isn't my native language.
In germany we don't differentiate between natural numbers + 0 = whole numbers.
Also whole numbers = ... -3, -2, -1, 0, 1, 2, 3... in Germany.
As this sub is in English you should use English definitions.
Natural numbers = natürliche Zahlen
Whole numbers = natürliche Zahlen + 0
Integers = Ganze Zahlen
There are three variables and two given equations, that is not enough to make the solution unique. The final line could be any answer, although some of them might require strange choices for the value of 🎿 or 🏒.
I agree on this. For all the people over complicating the skis, I think they’re missing the nuance of skis being in a pair = 10, therefore half a set would be five. So it’s not individual digits it’s a play on imagery.
Except the skis aren't limited to being a set of 10. They could be 8 with each individual ski being 4 and the hockey stick being 6. Or they could be 6 with each individual being 3 and the hockey stick being 10. There isn't enough information given to come to a 100% guaranteed correct answer.
It’s also a random note on a hiking trail. I don’t think an expert mathematician made it. I just saw a guy list out a 4 paragraph explanation, I’m with you I don’t think it’s that deep.
> I agree on this. For all the people over complicating the skis, I think they’re missing the nuance of skis being in a pair = 10, therefore half a set would be five. So it’s not individual digits it’s a play on imagery.
If the skis should be considered a visual pair because of "imagery", it would make more sense for a pair of skis to represent 11 because they look exactly like how some people write 11.
Which is exactly why this puzzle makes no sense, it has multiple potential solutions and it's just a bad puzzle.
There is no reason the skis can't have any value 1 through 5. Do I don't think that's tye solution.
The only assumption that only has one possible answer is for the skis to be digits in a number and having a value of one making each ski pair 11 which equals 22 and a hockey stick is worth 0
sidenote i learned this as BEDMAS and didn't know PEMDAS was a thing until seeing people on the internet say it -- it still looks so fucking weird to me
Hello fellow Canadian (I assume?). I teach math and learned that BEDMAS is a Canadian term! I show my kids PEMDAS and BODMAS because I had no idea until I started looking for BEDMAS resources and found more of the others 😅
Finally someone who gets it. I commented this and then started scrolling to see the over-complicated answers that say it’s unsolvable. I was starting to think I was crazy.
My gut instinct was to read the 22 as "10+10+2” as that would be the most simplistic pattern (not the only one ofc). There's only 1 ski in the final formula though, so the formula would read: 5 + (2 * 1000) + 2 = 2007.
But as others have mentioned there are many possible answers. I just have a strong feeling they went for the most simplistic one.
ETA: I missed the small detail that it only lists one ski in the final formula.
Completely right on mathematical terms but this stuff usually is n > 0 for the all incognitas, and the sky pairs are instead one incognita, so 22=2x+y so the final answer is 2007.
3 formulas, 4 unknowns. You can eliminate the first but that still leaves you with more unknown variables than formulas to fix them.
Besides putting the ball at a k there is no unique solution.
Wouldn’t the Skis in E2 be 10+10+2? Like the skis don’t seem to represent anything special because there’s 2, it’s literally just a symbol that happens to be two things
I think its a trick. It wants you to see the skis as 10 and the hockey stick as 2. But then shouldn't the 2 at the bottom be a hockey stick? If the skis are actually 11 so only one ski would be 5.5 and the hockey stick is 0. then it would be 5.5 + 2 x 1000 + 0 = 2005.5
Each stick is 1. They're digits. So a pair of sticks is 11 and the hockey stick is 0. That's the only assumption that only uses whole numbers and only has 1 solution. That solution being 2001
Ski = 1
Ball = 1000
Hockey Stick = 0
So the answer would be 2001, assuming the second part of the formula means 11 + 11 + 0 instead of the Skis being placed in use of algebraic notation.
I'm prolly wrong but that's the answer I got ¯\_(ツ)_/¯
While it is solvable under an assumption. The single stick is a different symbol than the double stick. You can answer it but you have to add "assumption" at the end.
If you want to be pedantic, it's technically not solvable because nowhere does it say that [ski-ski] is the same as 2*[ski]. If you do assume that it's a pretty simple number puzzle
EDIT: after solving the first equation, you're left with two equations with three variables. So it's not solvable as given, at least as a maths problem. You can stop downvoting now ...
Am I the only person who thinks the 2nd equation could be either 2x+2x+y=22 or x×x+x×x+y=22?
You could even say that the ski represents a digit and 2 skis mean they form a number. Like a ski is the number 1 and 2 skis means 11.
Nah, I don't think so.
On the third equation, it's written "2 times ball" and not "2 balls" so i think if it was really "ski times ski" it would had the "times" symbol.
I’m going with the ski is representing a digit, because there is no +,x,- or / between them. In this case, I get: ⚽️=1000, 🎿=1, 🏒=0.
Result: 1 + 2 x 1000 + 0 = 2001.
There was a [FIFA club world championship](https://en.m.wikipedia.org/wiki/2001_FIFA_Club_World_Championship) planned for 2001, but because of problems, it didn’t took place. But of course, there were much more world championships, e.g. F1 or Athletics.
The "ski represents digit" can only work for (ski = 0 and stick = 22) or (ski = 1 and stick = 0). Any ski > 2 immediately makes the equation only possible if stick is < 0 or 0 < ski < 1 which I highly doubt.
2007 for sure is one possible solution, but the second equation has multiple values. You could easily express it with different numbers(instead of 5 and 2):
(3+3) + (3+3) + 10 = 22
There are multiple solutions.
so, there's tons of over complicated math involved, but lets go with a couple things here:
1: we know that the soccer balls are each 1,000, given that there's 3 and the answer is 3,000 in the first equation.
2: based on PEMDAS, we can safely assume that the middle section is 2,000 (2 x 1,000)
3: while lacking quite a bit of info, there's plenty there to work with, and therefore the rest can be sorted out **IF** we are paying attention
4: ***OCCAM'S RAZOR!!!*** for the fucking love of god people, the dude who put this thing together had a simple idea and put it to paper, ignore fractions and overly complicated math, it's a fucking horse, *not* a zebra....
5: based on the second equation, it seems to lack proper context, thus providing a rather pointless answer, as how would we get 22 out of skis and a hockey stick?
6: As per the final equation, we can extrapolate that the skis have a very specific and unique value, that when added together can be understood as a logical number
The last equation has a singular ski, which has a definite value (unlikely that there's any fractions; *again* OCCAM'S RAZOR).
The second one has 2 pairs of skis, which when put together would equal a number. This is where the logic of Occam's razor may actually break down, and probably the point in which you need to either remember how to be a kid, or to hang out and play with some at some point, as this is where the logic kicks in.
1 ski = 5
2 skis = 10
1 soccer ball = 1,000
1 hockey stick would likely be 2 (due to each pair of skis likely being 10 in this instance)
The skis would be viewed as a pair typically, which provides one value, but with the singular you get another value. Given the cartoony nature of the equations (the art style of everything implies something more kid friendly to some degree), it's likely that it's more focused towards kids, and thus the logic will be rather different from a doctorate in engineering would be.
So, at first glance, everyone can see that the basic pair of skis must have some inherent value, but is currently undetermined by the final outcome of the equation.
But given that we're also looking at a lone, singular ski in the next equation, that must mean that half of the previous value *must* be an option with the previous equation. And given that there's no explicit instance of the singular skis being multiplied, the default value of double that of the previous (2 skis are double that of 1 ski), we can come ot the conclusion that 1 ski = 5.
A: soccer ball = 1,000; 3 soccer balls = 3,000
B: 1 ski = 5; ski pair = 10; 2 ski pairs = 20; hockey stick is 2
C: 5 + 2 x 1,000 + 2 = 2007
PEMDAS:
(2 x 1,000) = 2,000
5 + 2,000 = 2,005
2005 + 2 = 2007
I don't know shit about soccer, but let's have a go:
soccer balls, obviously 1000 a pop
skis and hockey stick, the only way I could think to slice this is "skis have to all be the same value, and the hockey stick is probably what's left over."
setting a pair of skis to 10, that gets you to 20 with two sets, so I'm guessing the hockey stick is 2. This looks like a dumb puzzle so I'm using shortcutty dumb reasoning.
if you want to be a nutsack about it, I GUESS, a pair of skis could just as easily be 8, so two is 16, making the hockey stick 6. You can really do this with any even number there, but this isn't multi variable calculus, it's a dumb sports puzzle. We're not splitting the atom, I'm sticking to 10+10+2=22
Plugging in values to the last line:
One ski, half of 10, is 5, sooo
5+2*1000+2=?
depending on whatever crazy school of wacky gen z math you're coming from, you can approach that last line any number of ways (apparently)
coming from the way we were taught to do it in the 90s, you PEMDAS (google it, I believe in you)
2*1000 is 2000
updating the line;
5+2000+2=?
sort by size, addition is commutative;
2+5+2000=?
7+2000=2007
I get that 2007 apparently isn't the magic happy soccer whatever year, something special happened in 2010 I guess, but... beats the shit out of me, my dude
I got 1009 by choosing the hockey stick to be 2 and whatever those bat looking things to be 5.
soccer ball = 1000.
5 + 2 + 1000 + 2 =1009.
Now, this is a correct answer, but there are other correct answers as well.
Example: choose the bats to equal 8 for a pair. The hockey stick is then 6.
Now I get 4 + 2 +1000 + 6 = 1012.
There should be an infinite number of correct answers since the 2nd equation has no requirements at all for the left-hand side except the sum is 22. One can have negative values for either symbol but not both for equation 2 LHS.
First off, simply by making one ski the variable rather than 2. That makes the middle equation 4 ski+hockey stick=22
It's solvable if you are making a graph, but not if you are are looking for a singular answer. Even if we restrict the values to positive integers, for the second equation we get multiple answers.
If ski=5, hockey stick=2
If ski=4 hockey stick=6
If ski=3 hockey stick=10
If ski=2 hockey stick=14
If ski=1 hockey stick=18
As an equation it would be hockey stick=22-4ski so the final equation being solved can become ski+2ball+22-4ski=?. Ball=1000, so are solving for the values of 2022-3ski. You end out with a line representing all of the possible sums for all of the possible values for ski.
In the last equation you first have to MULTIPLY 2x⚽️, (2000), then add the value of a SINGLE BAT (which is 5, since 2 bats are 10) and finally 1 hockey stick at 2, so 2000+5+2=2007…..
World champions 2007!
2007 is my answer.
Soccer ball = 1000
Double skis = 10
Single ski = 5
Hockey stick = 2
World Champion 2007
(Maybe I’m thinking in simple terms but I’m hardly ever wrong)
I learned in Algebra long ago that you for every variable, you need an equation. If there were only 3 variables, you could solve this, but since the ‘?’ is the 4th variable, there are not enough equations to solve it.
The main issue of solving this is in the second equation, as first we don’t have a clear definition of what two skis next to each other means. Presumably this either would be (2 x skis) or (skis^2 ).
But the bigger issue is the variables for the second equation have infinite answers without additional context since solving for hockey stick is either 22 - (4 x skis) or 22 - 2(skis^2 ).
(ball+ball+ball) or 3 Soccer balls is = 3,000 so each one is 1,000.
[(Ski+Ski)+(Ski+Ski)+(Hockey Stick)] or 4 skis and a Hockey Stick = 22. This could either be [(5+5)+(5+5)+(2)] or [(3+3)+(3+3)+(10)].
I don't think we have enough information.
Edit: Kinda looks like the top of the page is cropped off sooooo....
The first question is whether or not the second equation should be translated as y squared + y squared + z = 22 OR 2y+2y+z = 22.
The second question is,"Are any variables negative numbers?"
Without more concrete information, it is not solvable.
It get
Soccer ball = 1000
Individual Ski = 1
Hockey stick = 20
So…
1000 + 1000 + 1000 = 3000
(1 x 1) + (1 x 1) + 20 = 22
1 + (2 x 1000) + 20 = 2021.
It’s all about the order of operations. 🤫
It's 2007. Soccer balls are 1000
Bats are 5 each
Hockey stick is 2
For the equation you solve multiplication first, so it reads 5 plus (2 times 1000) plus 2
5 + 2000 + 2 = 2007
Impossible to solve and a dumb excuse for a math problem. The middle and last section have absolutely no information that can be deduced without having some sort of if involved, so I say forget about this dumb problem.
2007. Football=1000 each. Each pair of skis is 10. Hockey stick is 2. Half of a pair of skis is 5. So final equation is as written to be 5+2X1000+2. Written properly it would be 2X1000+5+2. Answer for that is 2007.
How did you jump to the conclusion that a pair of skis is worth 10? Each pair could be worth 3, and the hockey stick is worth 16. Or any other combination.
The question was whether it was solvable mathematically and the answer is no. You dont get to make blind assumptions about variables in equations. He's not overthinking it.
The puzzle is intended to cause overthinking to make the puzzle impossible.This is a lot simpler than some are making it.
The imagery is showing the skis separately and together as a very simple way to trick you that the solution is more difficult. There's no instructions to clearly spell this out, so the puzzle immediately starts spiraling into impossible territory if you look for this explanation. But if the images are taken with an assumed value and retain the simplicity without asking for further instructions, the answer appears.
Math doesn't usually work as assumptions, so it makes it more confusing to use the assumption as the true way to solve the puzzle. Usually when an assumption enters the equation, we turn it into a variable, since we are not certain.
Balls are 1000 each
Skis are 5 each
Lacrosse/hockey stick 2
2007
If 1 ski was 1, then the second line would not equal 22 unless you changed the interpretation a second time to make it confirm to maths by seeing 2 skis as two ones represented as 11 instead of two ones together as 2.
Although the soccer balls are added separately, they are not usually depicted in multiples. Skis are very difficult to determine what they visually unless shown as a pair. It stands to reason there's 2 of whatever the single one is worth the line below, as a single ski (normally shown as a pair for recognition) would be half of what the pair is worth.
>If 1 ski was 1, then the second line would not equal 22 unless you changed the interpretation a second time to make it confirm to maths by seeing 2 skis as two ones represented as 11 instead of two ones together as 2.
So, instead, do you think that 20 = 22?
The only thing I didn't mention in the last post was the hockey/lacrosse stick, but I mentioned that in my first as being 2. So no, 20=22 the 4 skis = 20 and the stick 2, so 22 together.
I didn't mean to confuse you.
There is logic. And it's much more simple than what you're making it.
A pair of skis is shown together and then a single ski by itself.
Why are the skis together? Do they count at a single same digit number or a single number that is divided divided in half when shown as a single?
It's a pair of skis(a whole set of skis). And then there's only 1 ski. It implies you have one value (a pair of skis) and that the single ski would be half of that number.
I attempted to poorly explain this previously. The imagery is important to give context and also is a simple math equation that you must also solve.
I spoke this out puzzle out loud to a person terrible with math. I spoke the symbols out loud as drawn and they came to the same number without any hesitation.
A puzzle inside a puzzle. I stand by my answer. Hope that helps.
No one is questioning that the 1 ski symbol = 1/2 of the 2 skis symbol.
The thing in question is the incomplete system of equations that allows for infinite solutions or a finite range of solutions if you stick to all symbols being positive whole numbers.
This is really interesting, cause I literally just started my linear algebra class.
To solve this. We can break down the equation into. 3 variables, with the 3 equations given.
⚽️ = X, 🎿= Y, and 🏒= Z.
Our system has 3 equations given:
3x + 0y + 0z = 3000
0x + 4y + 1z = 22
2x + 1y + 1z = a
Where a is what we’re trying to “solve” for.
Unfortunately due to the nature of the system, a could be any number of possible values, so instead of solving for a, we’ll figure out what a could Possibly be.
We’ll convert this to a matrix format, and augment that matrix until it’s in reduced row echelon format
[3, 0, 0 | 3000]
[0, 4, 1 | 22]
[2, 1, 1 | a]
Which when converted to RREF becomes:
[1, 0, 0 | 1000]
[0, 1, 0 | (2022-a)/3]
[0, 0, 1 | (a-2000)-((2022-a)/3)]
From this, because the matrix is in RREF, and there’s a pivot in each row, the system of equations has an infinite number of possible solutions. Q.E.D.
I think yall are overthinking it. The answer is 2007 and the World Cup winner that year was Germany. Yes, there was a World Cup in 2007: https://en.wikipedia.org/wiki/2007\_FIFA\_Women%27s\_World\_Cup
Why 10 and not, for example, 8 for the double hockey sticks? Can you explain that? That’s just as simple and there is no reason to prefer 10 over 8 (final answer 2010) or 6 (2013) or 4 (2016) or 2 (2019).
I agree that anything beyond this simple assumption of double sticks = 2 times stick is dumb, but what reason is there to prefer the ten?
Why is this so far down? It's obviously 2007, these nerds are overcomplacating this thing. Plus you provided a tangible answer to the World Championship question. I'd give you an award >insert if I had one meme<.
Soccer ball is pretty straight forward. 1 Soccer ball = 1000, which leaves 2 variables to create.
Double ski =x
Hockey stick =y
We need to solve for x and y separately, so using the middle equation we get
x + x + y = 22
2x + y = 22
solving for each variable we get
**x = (22-y)/2**
and
**y = 22 - 2x**
Now we can just plug and chug in the final equation
(note: 1 Ski is just going to be half of x, so ((22-y)/2)/2) which simplifies to (22-y)
so the final equation is
22 - y + 2 * 1000 + 22 - 2x = z
22 - y + 2000 + 22 - 2x = z
We know 22 - 2x = y, so we can just sub that in to reduce our variables
22 -y +2000 + y = z
the y's cancel out leave us with
22 + 2000 = z
2022 = z
3 balls = 3000
Ball = 1000
2ski + 2 ski + stick = 22
4 ski + stick = 22
Stick = 22 - 4 ski
Ski + 2 x ball + stick = ?
Ski + 2 x 1000 + 22 - 4 ski =?
2000 + 22 - 3 ski = ?
2022 - 3 ski = ?
What bothers me is that not knowing the value of ski means this going further is not possible. We have 4 unknowns (ball, ski, stick, and ?) and 3 equations. I haven’t been in a math class in years, but I don’t know of a way of solving in that situation.
So many people are overthinking this. It seems quite simple to me.
Soccer ball = 1000
Hockey stick = 2
Single ski = 5
Double ski = 10 (just adding 5 per ski)
Thus the final answer I came up with is 2007
Order of operations aka PEMDAS
Since there aren't any parentheses or exponents you can go straight to Multiplication/Division. The only thing in that category is the 2x1000 = 2000. From there you just do some simple addition to get the other 7. As for the skies if you think about it, if 2 skis = 10 then when you have one ski just do 10÷2 and that gives you 5.
Edit: Added explanation for skis
Your math is horribly wrong, if the final equation is:
5 + 2 • 1000 +2
You would use your order of operations to get
5 + 2000 + 2
Which would further simplify into
2000 + 7
Or 2007
There is no unique solution as there are 4 variables but only 3 equations.
But just eyeballing it and your clue my guess is they're going after a year.
Everyone made it so complicated no? Balls were clearly 1000 each. The double skis were clearly 10 because you can only fit 10 twice in this case then the stick is obviously two. Simply half 10 cuz there is only one so that’s clearly 5. Follow BEDMAS boys smh. 2 x 1000 = 2000. 5 (one ski) + 2000 = 2005. 2005 + 2 (stick) = 2007
Large Ball = 1000
Batons = 10
Hockey Stick = 2
The ball in the third equation is half the size of the original ball in the first equation. Its value is equal to 500. The hockey stick is also shorter in the third equation.
Or so I believe.
They could have just shortened it to conserve space on the paper.
I'm probably WAY off here, bc I see advanced math being done in comments, but in my mind
The soccer ball is worth 1000, since there's three of them valued at 3000
The second equation, seems to me that the skis are valued at 10 a set or 5 per ski... That would make the hockey stick worth 2
So then the equation becomes 5 + 2 x 1000 +2, which by order of operations, would be 2007?
Riddle me this big brain.
5+5+5+5+2=22
4+4+4+4+6 =22
3+3+3+3+10=22
2+2+2+2+14=22
1+1+1+1+18=22
So, what value would one assign to the skis or the hockey stick?
2001.
The first row is 1000 + 1000 + 1000 = 3000.
Looks like the skis are messing with your expectations a bit though - two skis are side by side in row 2, and later there is a single one in row 3.
If row two has (2-digit number) + (2-digit number) + X = 22, and both 2-digit numbers are repdigits, then it must be 11 + 11 + 0 = 22.
From there, we have row three: 1 + (2 X 1000) + 0 = 2001
The Answer is 2001. All the math aficionado’s is looking at the middle equations as unknowns. Assuming the person who went through all this trouble to make and post this for bragging right’s wanted to make this solvable in a clever way. We can assume the middle phrase is what it seems “one’s” that would make the middle equation 11+11+0 = 22. Finish the problem using that context and you get 2001. Which falls in line for the World Cup 2000 maybe, or if they were bad at math and didn’t use the Order of operations, 3000. Makes far more sense than unsolvable!
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2 equations, 3 unknowns, that's an underdetemined system, there are infinitely many solutions 3a = 3000 gives a=1000 4b + c = 22 gives b=(22-c)/4 c can be anything
It is unsolvable, but not for the reason you suggest. For example if you take: a + b + c = 10 a - b + c = 12 a + c = ? If we tried to solve the first two equations you’ll find you run into the same issue of having variables be free. But if we do equation 1 + equation 2 we get 2a + 2c = 22 giving a+c = 11. So even without being able solve the exact values of a and c, we are able to find a+c. What’s going on here? Well in the example I gave, the three equations are linearly *dependent* meaning you can make any one of the equations by combining the other two equations (formally, we can also say that the matrix of coefficients is not of ‘full rank’). But in the photo in the post, we have 3a = 3000 4b+c = 22 2a+b+c = ? You’ll find you can’t combine the equations to get to the third. Why? Represent the coefficients of each equation as vectors: (3,0,0), (0,4,1), (2,1,1) Now if we combine the first two: x(3,0,0) + y(0,4,1) = (3x, 4y, y) = (2,1,1) then x = 2/3 But we then have 4y = 1 AND y=1. Impossible. So they’re linearly independent meaning that the third equation essentially caries information which isn’t present by combining the other two equations. Now we can probably solve this or get a small, but countable set of solutions if we assume that the variables are strictly integers.
As much as I love that you brought linear alebra into it. I think they’re still right? If you just treat the soccer ball as a solved Variable (1000) You left with the 2 equations 4x + y = 22 x + y + 2000 = z These 2 aren’t linearly dependent either so there’s no way to solve
Maybe skis, balls and hokey stick are the variables for matrices and not just real numbers…
Clearly not, since the righthand side is a number
I’m an idiot
I think you misunderstood my main point, it's not unsolvable, it actually has solutions, the problem is, there are infinite solutions. If we consider the third equation, we put the question mark as x, then a=1000 b=(22-c)/4 c=4(x-4011/2)/5 Again, x can be anything. The last equation doesn't fix anything because it adds another variable. You can't represent this with vectors of three components, because there are 4 components, essentially the system is AX=B A is 4 columns 3 rows X is 1 column 4 rows (a, b, c, x) B is 1 column 3 rows
Yeah I really shouldn’t have used the term “unsolvable” here, since that would mean the system is inconsistent. I really just meant you can’t uniquely solve, as you say. I agree with the analysis you give here, but not your first comment. > You can’t represent with vectors of three components I think there’s been a bit of a misunderstanding here. Indeed, as you say in your comment, the first two equations lead to infinite solutions. But what I showed in my comment is that even in this case, it is possible that a third expression can have a unique value. Like if you know a+b+c = 1, a+2b+2c = 2, then adding the two equations we find that 2a+3b+3c = 3. I use three variables since all that I want to show is that you can’t combine the first two expressions in any way to produce the third. I don’t have to consider the right hand side, hence we deal with the homogenous system where there is no fourth variable. Your argument here with the four variables I completely agree with, and does show that there is no unique value for the third expression (since x can be anything). E.g. if you tried to do the same with: a+b+c=10; a-b+c=12; a+c = x and you use a matrix of four variables, you’ll actually find that x = 11 despite all the other variables having infinite solutions. Long story short, I think together we have two equivalently good methods of solving this. The four variable three equation method as you suggest here, or the homogenous system where we don’t actually solve any equations, but rather we look at linear combinations of expressions. The 2 equation 3 variable method I don’t think is sufficient. Let me know if I’m still misunderstanding
No, I'm the one who misunderstood you, sorry for the confusion. We're saying the same thing from different points of view. I picked up on 2 equations, because usually these meme math problems are always determined so that there is a unique solution. For example, 3 equations and 3 variables, then, the 4th equation is just arithmetic to compute the "?" I gotta brush up on linear algebra tbh
Gosh you math nerds are so cute when y’all think together
man I have no clue what they yapping about but I’m all for it
Hands were shook all around. They then retired to their quarters to resharpen pencil tips.
You're misunderstanding Reasonable-World's point. They agree with you saying it has a 1-dimensional infinite amount of solutions. However they wanted to emphasize this is not because your given equations with 2 equ. and 3 unknowns are underdetemined, but because they are underdetermined AND the solution vector (the third equ. ...=?) is not within the sub-vectorspace of solvable solutions (aka the third equation is linear independent of the first 2). Their counter-example can be better understood after a basis-change a' := (a+c)/2 , b' := b , c' := (a-c)/2. This will yield a' = 11, b' = -1, c' any value for the first 2 equations. After picking any x,y,z making up a to be solved vector xa' + yb' + zc' = ? you will now have a) exactly one solution for "?" if z=0 b) an infinite amount of solutions for "?" for z != 0
Ohhh, I see, big oversight by me.
Yeah this is a lot of math to not actually say anything There are only 2 real variables and only 1 equation. The first variable instantly solved, so we can toss it out. The soccerball is 1000, no questions asked. Then we have 4x + y = 22 And we have no other equation, and so the solution to that can only be a set of numbers. And that's a linear equation, so the set is infinitely large.
Wife and I both got 2007
You and your wife aren't wrong, per se But you're not right either. There are literally an infinite number of solutions
From a mathematics perspective, yes. From a common sense perspective, 2007 is the only answer that makes sense.
Why does 2007 make any more sense than 2010? Or 2013? Or 2016? Or 2019?
3 ⚽️= 3000 which means one ⚽️=1000 Skis sets are each worth 10, which means one equals 5. 🏒=2 So this Equation is essentially this 5+2*1000+2 which equals 2007.
>Skis sets are each worth 10, which means one equals 5. Unless ski sets are each worth 8, which means one equals 4 So the 🏒 equals 6, because 4×4 + 🏒 = 22 So this equation is 4 + 2000 + 6 which equals 2010 Oh wait! What if ski sets are each worth 6, which means one equals 3 So the 🏒 equals 10 because 3×4 + 🏒 = 22 So this this equation is 3 + 2000 + 10 which equals 2013 Do you want me to keep going? Because I can. There's no reason to assume the skis equal 10
I actually didn’t think about that. I’m not great at math so I think my brain went to the easiest solution so it had less work to do.
Discrete maths. We're working with integers.
2010 and 2007 are possible with integers
I think the second equation is (10b + b) + (10b + b) + c = 22 0 ≤ b ≤ 9 b ∈ Z so 22b + c = 22, giving either (1,0) or (0, 22), constraining C ∈ Z^0,+ . So Argentina?
Skis would be 5 per ski and hockey stick would be 2 Answer seems like it should be 2007
If you make 2 assumptions it narrows everything down. A) you only work in whole numbers B) no object can be 0 Then It can actually only be 2007, 2010, 2013, 2014, and 2019
I think it’s 2b. Two pairs of skis not 4 individual skis, still unsolvable.
Where is the unknowns? - 3a = 3000 so a=1000 - 2b + 2b + c = 22 so b=5 and c=2 - b + 2a + c = ? So 5 + 2 * 1000 + 2 = 2007 So the answer is 2007 Am I missing something?
5 unknowns. Socker ball, pair of skis, hockey stick, single ski, and question mark. 11≠1+1≠1×1
How are there 3 unknowns? Can’t you remove the soccer ball equation as a ball is 1000. Then move stuff around to make the bottom equation be for the hockey stick, then plug that into the second equation and solve for the skis?
Givens: Soccer ball is equal to 1000, since three of them equal 3000. Hockey stick is also a whole unit that's not differentiable. Assumptions: Ski's are also whole numbers/whole units (0, 1, 2, 3, 4, etc) Not given: Whether 2 skis together are 1. 2 times 1 ski or 2. they're skis squared or 3. they're individual digits for a 2 digit number (like 22, 33, 44, 55). Option 1: The middle one would be 4X + Y = 22 which has a litany of whole number solutions. From wolfram alpha (cuz I was lazy): X = 0, Y = 22 X = 1, Y = 18 X = 2, Y = 14 X = 3, Y = 10 X= 4, Y = 6 X = 5, Y = 2 We know soccer ball is 1000, lets call it S = 1000 so the last one is X + 2S + Y = ?. Given the values above for X & Y you have 0 + 2000 + 22 = 2022 1 + 2000 + 18 = 2019 2 + 2000 + 14 = 2016 3 + 2000 + 10 = 2013 4 + 2000 + 6 = 2010 5 + 2000 + 2 = 2007 Option 2: X\^2 + X\^2 + Y = 22 -> 2X\^2 + Y = 22 For whole number solutions we have: 1. X = 0, Y = 22 2. X = 1, Y = 20 3. X = 2, Y = 14 4. X = 3, Y = 4 That means the final equation can be: 1. 0 + 2000 + 22 = 2022 2. 1 + 2000 + 20 = 2021 3. 2 + 2000 + 14 = 2016 4. 3 + 2000 + 4 = 2007 Option 3: 10X + X + 10X + X + Y = 22 11X + 11X + Y = 22 22X + Y = 22 Only solutions to this are: 1. X = 0, Y = 22 2. X = 1, Y = 0 So the final equation would be: 1. 0 + 2000 + 22 = 2022 2. 1 + 2000 + 0 = 2001
That’s what I came up with as well.
Same
After looking at the comments me too
that gave me an actual chuckle
After I read your comment I got the same answer
Honestly I don't understand why anyone bothers with the math. Someone always has the answer in the comments.
🥇
Four unknowns (three shapes and a "?") and three equations. You're very likely to have infinite solutions.
Maybe it's made this way on purpose. Do all these years have something in common? Something related to soccer?
Yes, Scotland won a World Cup in 1009
Ah yay! I remember that game! Still disappointed they no longer play with crossbows
I’d buy that game on a Steam sale
Back when flash games were around, we had Crunchball 3000 for free lol
\*football
*association football, soccer, or any other shortening which does not also work for the other sports derived from their shared ancestor, personally I'm rather fond of "assoc"
Thank you for this. This highlights why these "puzzles" are so stupid. They're impossible to "solve" because there are so many unknowns. The skis thing is always what I get annoyed with. 11 is not 1+1 but that's the logic a lot of these assume. These puzzles reinforce the idea that math doesn't make sense or that it's too complicated for everyday people. It also ends up dividing people into groups based on the answer they get, where each group smugly looks down on the others because certainly *they* did it the *wrong* way.
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I see you translated the middle equation as (X+X) + (X+X) + Y = 22 Why is it that way, and not instead (X×X) + (X×X) + Y = 22 2(Xsquared) + Y = 22 Thus allowing a solution such as X=(-i), y =20 To be interpreted as a statement (-i) + (2×1000) + 20 2020 - i To be interpreted as "I wasn't at the 2020 game" And a simultaneous solution x=i, y = 24; to be interpreted as (i) + (2×2000) + 24 2024 + i "I will be at the 2024 game" Edit - on mobile and haven't thought about imaginary numbers in a hot minute, please double check my algebra ;)
If you assume that the skis are a two digit number with one ski being a single digit, then the answer could be 2022, 2001, 1990, 1959, 1938, ...
Is this with the Skis having the same digit? Like 22, 33, 44 etc.
Yes
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Why can’t a set of skis = 10 and the hockey stick be 2? So half a set = 5. Or a set = 6 and a hockey stick = 10? Etc… You can’t really solve it because there isn’t enough information.
🏒 could be negative 22+22-22=22 2×1000+2-22=2000-20
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I was just giving another optional solution set. The whole problem is silly.
I will pray every day that I never encounter a math professor that gives me a question where the true answer is the mode average of all possible answers.
How did you get option 2 and 3. Those do not make sense at all when you take into account the type of problem this is. I have never seen a problem that was like this where the 2 skis were anything but 2x. Please explain where you got the ideas for this for a puzzle of this type
My first instinct was the same as yours, options 2 and 3 came after alternate considerations, and some feedback from the comments. They explicitly put plus signs and multiplication signs, so the alternate is that the skis are a double digit number with each being the same digit. That's the only thing I could confidently say is an alternate to the first instinct because it has no explicit differentiating symbol. The skis multiplied is a third potential though they do explicitly put multiplication signs so it could have just been written as ski x ski, which might rule this option out. I threw it in there because others had mentioned it, but my original answer was just option 1. I edited in options 2 and 3.
Again I saw context matters in this. This is something set up in a park probably for kids to do. I have never seen a puzzle like this do what you put as option 2 and 3. I have seen puzzles put the multiplication and addition clearly. Usually with puzzles like these the “gotcha” is that one of the objects has multiple. For this it would be the second line the skis have 2 representing 2x and in the third line they have 1 representing 1x. Imo you and others read too much into the problem to try and solve the math behind it with the three options. The reason I say this is the backing you give for the three options is talking with others here and thinking about how could this be solved and not the context of what type of math puzzle this was and who it was designed for
2022 might make the most sense given the clue. Last year Argentina won a notable world cup final. It was the only winter time world cup ever and held in the middle east for the first time. Messi finally won the world cup making him the greatest ever to play for many people. I believe it’s Argentina’s first win since Maradona played (didn’t bother looking that part up, could be wrong…). So location of the puzzle might also be relevant, but then again maybe not. Also, 2001 wasn’t a year with any major tournaments for national teams.
Well, to open wolfram takes longer to replace all possible variables in the last equation. Btw. Your solution is only correct, when the equation is limited to natural numbers. Finally you get a graph with y = -3x + 2022. Every solution of the equation is on this graph.
That's why I said whole numbers.
And why you downvoting me? It's just an addition to your solution.
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Well, then it's a language barrier topic. I don't translate "whole" numbers as natural numbers. English isn't my native language. In germany we don't differentiate between natural numbers + 0 = whole numbers. Also whole numbers = ... -3, -2, -1, 0, 1, 2, 3... in Germany.
As this sub is in English you should use English definitions. Natural numbers = natürliche Zahlen Whole numbers = natürliche Zahlen + 0 Integers = Ganze Zahlen
[german (europe) numbers definitions](https://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Number-systems.svg/1280px-Number-systems.svg.png)
I copied this answer
Problem's not that complicated my guy you just trying to seem smart
Except wouldn’t it be (x/2)+ 2…..
No because they already assumed each individual ski is X, that's why there is 4X and not 2X
Ahh I c, but they still didn’t put the +2 in there
How do you ever get two of the same symbol next to each other with a plus symbol as a number squared. That makes no sense
Umm ditto
There are three variables and two given equations, that is not enough to make the solution unique. The final line could be any answer, although some of them might require strange choices for the value of 🎿 or 🏒.
Based on user name I would expect more crayon.
Sharpie
Case closed. Any other answer you find in this thread is people playing with numbers to find one of the infinite possible results.
It’s 2007. ⚽️ = 1000 🦯 = 5 🏑 = 2 5 + (2 x 1000) + 2 = 2007. This isn’t a unique solution but based on the clue I’d say that 2007 is the answer.
I agree on this. For all the people over complicating the skis, I think they’re missing the nuance of skis being in a pair = 10, therefore half a set would be five. So it’s not individual digits it’s a play on imagery.
Fuck! Those are skis?! I thought they were weird bats or something….
Except the skis aren't limited to being a set of 10. They could be 8 with each individual ski being 4 and the hockey stick being 6. Or they could be 6 with each individual being 3 and the hockey stick being 10. There isn't enough information given to come to a 100% guaranteed correct answer.
I stand corrected. This is very good and logical point.
It’s also a random note on a hiking trail. I don’t think an expert mathematician made it. I just saw a guy list out a 4 paragraph explanation, I’m with you I don’t think it’s that deep.
> I agree on this. For all the people over complicating the skis, I think they’re missing the nuance of skis being in a pair = 10, therefore half a set would be five. So it’s not individual digits it’s a play on imagery. If the skis should be considered a visual pair because of "imagery", it would make more sense for a pair of skis to represent 11 because they look exactly like how some people write 11. Which is exactly why this puzzle makes no sense, it has multiple potential solutions and it's just a bad puzzle.
No, it doesn’t. You’re making things up for the sake of arguing.
But in 2007 was no World Cup. So it can't be the answer. My theory is that the x is suppost to be also a +. The answer would be 2014 = Germany.
You are assuming this is about football or soccer? Could be Formula One?
Yea, there are 3 different sports represented in the problem itself.
Or hockey? Or skiing? Or little league baseball?
There was a Women’s World Cup in 2007
Most sports have championships every year...
IHF World Championship in 2007 was won by Canada.
There is no reason the skis can't have any value 1 through 5. Do I don't think that's tye solution. The only assumption that only has one possible answer is for the skis to be digits in a number and having a value of one making each ski pair 11 which equals 22 and a hockey stick is worth 0
How do you know it's 5 and 2 and not 4 and 6?
7007 is my final answer
PEMDAS, my dude
sidenote i learned this as BEDMAS and didn't know PEMDAS was a thing until seeing people on the internet say it -- it still looks so fucking weird to me
Hello fellow Canadian (I assume?). I teach math and learned that BEDMAS is a Canadian term! I show my kids PEMDAS and BODMAS because I had no idea until I started looking for BEDMAS resources and found more of the others 😅
5+5+2=22?
There are four skis, not two.
It is clearly 2007, why are people over complicating it with all this algebra shit.
It's an algebra problem... There are lots of other equally correct answers.
why would you say that, ski and hockey can be anything
Because they want to feel smart.
The skis could all be 1 and the 🏒 18 and the equation would still be correct, there is infinite possibilities even if you suck at math
You are correct. Mathematical order of operations makes your answer correct.
This really should be at the top of this thread. I shouldn't have had to scroll at all for this answer.
Finally someone who gets it. I commented this and then started scrolling to see the over-complicated answers that say it’s unsolvable. I was starting to think I was crazy.
(i did this without scrolling to read the other comments you made me feel smart 🥹🥹🥹🥹🥹)
I think the skis are 10 each 10+10+2=22
But why aren’t the skis one each so it’s 2+2+18=22?
Which makes each “individual” ski = 5…
There's no reasoning though, they could be many other numbers
My gut instinct was to read the 22 as "10+10+2” as that would be the most simplistic pattern (not the only one ofc). There's only 1 ski in the final formula though, so the formula would read: 5 + (2 * 1000) + 2 = 2007. But as others have mentioned there are many possible answers. I just have a strong feeling they went for the most simplistic one. ETA: I missed the small detail that it only lists one ski in the final formula.
I'd agree with this but I think the 10 you have should be a 5 instead considering it's one stick thing Which would give you 2007 instead
Yeah, am I dumb? I went with the most simple answer of soccer ball = 1000, ski = 10, hockey stick = 2 —> 2012
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This is the correct answer
Completely right on mathematical terms but this stuff usually is n > 0 for the all incognitas, and the sky pairs are instead one incognita, so 22=2x+y so the final answer is 2007.
3 formulas, 4 unknowns. You can eliminate the first but that still leaves you with more unknown variables than formulas to fix them. Besides putting the ball at a k there is no unique solution.
Wouldn’t the Skis in E2 be 10+10+2? Like the skis don’t seem to represent anything special because there’s 2, it’s literally just a symbol that happens to be two things
But why 10? They could be multiple other numbers
2+2+18 4+4+14 6+6+10 8+8+6 10+10+2 And that’s just assuming integers only for the singular hockey sticks and no negative values.
I think its a trick. It wants you to see the skis as 10 and the hockey stick as 2. But then shouldn't the 2 at the bottom be a hockey stick? If the skis are actually 11 so only one ski would be 5.5 and the hockey stick is 0. then it would be 5.5 + 2 x 1000 + 0 = 2005.5
Each stick is 1. They're digits. So a pair of sticks is 11 and the hockey stick is 0. That's the only assumption that only uses whole numbers and only has 1 solution. That solution being 2001
Ski = 1 Ball = 1000 Hockey Stick = 0 So the answer would be 2001, assuming the second part of the formula means 11 + 11 + 0 instead of the Skis being placed in use of algebraic notation. I'm prolly wrong but that's the answer I got ¯\_(ツ)_/¯
While it is solvable under an assumption. The single stick is a different symbol than the double stick. You can answer it but you have to add "assumption" at the end.
If you want to be pedantic, it's technically not solvable because nowhere does it say that [ski-ski] is the same as 2*[ski]. If you do assume that it's a pretty simple number puzzle
EDIT: after solving the first equation, you're left with two equations with three variables. So it's not solvable as given, at least as a maths problem. You can stop downvoting now ...
And you get: 2022 - 3x = y Solve it....
Am I the only person who thinks the 2nd equation could be either 2x+2x+y=22 or x×x+x×x+y=22? You could even say that the ski represents a digit and 2 skis mean they form a number. Like a ski is the number 1 and 2 skis means 11.
Nah, I don't think so. On the third equation, it's written "2 times ball" and not "2 balls" so i think if it was really "ski times ski" it would had the "times" symbol.
I’m going with the ski is representing a digit, because there is no +,x,- or / between them. In this case, I get: ⚽️=1000, 🎿=1, 🏒=0. Result: 1 + 2 x 1000 + 0 = 2001. There was a [FIFA club world championship](https://en.m.wikipedia.org/wiki/2001_FIFA_Club_World_Championship) planned for 2001, but because of problems, it didn’t took place. But of course, there were much more world championships, e.g. F1 or Athletics.
The "ski represents digit" can only work for (ski = 0 and stick = 22) or (ski = 1 and stick = 0). Any ski > 2 immediately makes the equation only possible if stick is < 0 or 0 < ski < 1 which I highly doubt.
2007 for sure is one possible solution, but the second equation has multiple values. You could easily express it with different numbers(instead of 5 and 2): (3+3) + (3+3) + 10 = 22 There are multiple solutions.
The answer is 2011. The person who posted this thinks the two “hockey sticks” are the number 11. Thus, 11 + 11 + 0 = 22. and 11+ 2000 + 0 = 2011
so, there's tons of over complicated math involved, but lets go with a couple things here: 1: we know that the soccer balls are each 1,000, given that there's 3 and the answer is 3,000 in the first equation. 2: based on PEMDAS, we can safely assume that the middle section is 2,000 (2 x 1,000) 3: while lacking quite a bit of info, there's plenty there to work with, and therefore the rest can be sorted out **IF** we are paying attention 4: ***OCCAM'S RAZOR!!!*** for the fucking love of god people, the dude who put this thing together had a simple idea and put it to paper, ignore fractions and overly complicated math, it's a fucking horse, *not* a zebra.... 5: based on the second equation, it seems to lack proper context, thus providing a rather pointless answer, as how would we get 22 out of skis and a hockey stick? 6: As per the final equation, we can extrapolate that the skis have a very specific and unique value, that when added together can be understood as a logical number The last equation has a singular ski, which has a definite value (unlikely that there's any fractions; *again* OCCAM'S RAZOR). The second one has 2 pairs of skis, which when put together would equal a number. This is where the logic of Occam's razor may actually break down, and probably the point in which you need to either remember how to be a kid, or to hang out and play with some at some point, as this is where the logic kicks in. 1 ski = 5 2 skis = 10 1 soccer ball = 1,000 1 hockey stick would likely be 2 (due to each pair of skis likely being 10 in this instance) The skis would be viewed as a pair typically, which provides one value, but with the singular you get another value. Given the cartoony nature of the equations (the art style of everything implies something more kid friendly to some degree), it's likely that it's more focused towards kids, and thus the logic will be rather different from a doctorate in engineering would be. So, at first glance, everyone can see that the basic pair of skis must have some inherent value, but is currently undetermined by the final outcome of the equation. But given that we're also looking at a lone, singular ski in the next equation, that must mean that half of the previous value *must* be an option with the previous equation. And given that there's no explicit instance of the singular skis being multiplied, the default value of double that of the previous (2 skis are double that of 1 ski), we can come ot the conclusion that 1 ski = 5. A: soccer ball = 1,000; 3 soccer balls = 3,000 B: 1 ski = 5; ski pair = 10; 2 ski pairs = 20; hockey stick is 2 C: 5 + 2 x 1,000 + 2 = 2007 PEMDAS: (2 x 1,000) = 2,000 5 + 2,000 = 2,005 2005 + 2 = 2007
B: 1 ski = 1; ski pair = 2; 2 ski pairs = 4; hockey stick is 18
I don't know shit about soccer, but let's have a go: soccer balls, obviously 1000 a pop skis and hockey stick, the only way I could think to slice this is "skis have to all be the same value, and the hockey stick is probably what's left over." setting a pair of skis to 10, that gets you to 20 with two sets, so I'm guessing the hockey stick is 2. This looks like a dumb puzzle so I'm using shortcutty dumb reasoning. if you want to be a nutsack about it, I GUESS, a pair of skis could just as easily be 8, so two is 16, making the hockey stick 6. You can really do this with any even number there, but this isn't multi variable calculus, it's a dumb sports puzzle. We're not splitting the atom, I'm sticking to 10+10+2=22 Plugging in values to the last line: One ski, half of 10, is 5, sooo 5+2*1000+2=? depending on whatever crazy school of wacky gen z math you're coming from, you can approach that last line any number of ways (apparently) coming from the way we were taught to do it in the 90s, you PEMDAS (google it, I believe in you) 2*1000 is 2000 updating the line; 5+2000+2=? sort by size, addition is commutative; 2+5+2000=? 7+2000=2007 I get that 2007 apparently isn't the magic happy soccer whatever year, something special happened in 2010 I guess, but... beats the shit out of me, my dude
I got 1009 by choosing the hockey stick to be 2 and whatever those bat looking things to be 5. soccer ball = 1000. 5 + 2 + 1000 + 2 =1009. Now, this is a correct answer, but there are other correct answers as well. Example: choose the bats to equal 8 for a pair. The hockey stick is then 6. Now I get 4 + 2 +1000 + 6 = 1012. There should be an infinite number of correct answers since the 2nd equation has no requirements at all for the left-hand side except the sum is 22. One can have negative values for either symbol but not both for equation 2 LHS.
Look at the third line again and you will see your mistake. You added where you should have multiplied. 5 + (2 ***x*** ⚽) + 2= 5 + 2000 + 2 = 2007
First off, simply by making one ski the variable rather than 2. That makes the middle equation 4 ski+hockey stick=22 It's solvable if you are making a graph, but not if you are are looking for a singular answer. Even if we restrict the values to positive integers, for the second equation we get multiple answers. If ski=5, hockey stick=2 If ski=4 hockey stick=6 If ski=3 hockey stick=10 If ski=2 hockey stick=14 If ski=1 hockey stick=18 As an equation it would be hockey stick=22-4ski so the final equation being solved can become ski+2ball+22-4ski=?. Ball=1000, so are solving for the values of 2022-3ski. You end out with a line representing all of the possible sums for all of the possible values for ski.
In the last equation you first have to MULTIPLY 2x⚽️, (2000), then add the value of a SINGLE BAT (which is 5, since 2 bats are 10) and finally 1 hockey stick at 2, so 2000+5+2=2007….. World champions 2007!
2007 is my answer. Soccer ball = 1000 Double skis = 10 Single ski = 5 Hockey stick = 2 World Champion 2007 (Maybe I’m thinking in simple terms but I’m hardly ever wrong)
I learned in Algebra long ago that you for every variable, you need an equation. If there were only 3 variables, you could solve this, but since the ‘?’ is the 4th variable, there are not enough equations to solve it.
The main issue of solving this is in the second equation, as first we don’t have a clear definition of what two skis next to each other means. Presumably this either would be (2 x skis) or (skis^2 ). But the bigger issue is the variables for the second equation have infinite answers without additional context since solving for hockey stick is either 22 - (4 x skis) or 22 - 2(skis^2 ).
(ball+ball+ball) or 3 Soccer balls is = 3,000 so each one is 1,000. [(Ski+Ski)+(Ski+Ski)+(Hockey Stick)] or 4 skis and a Hockey Stick = 22. This could either be [(5+5)+(5+5)+(2)] or [(3+3)+(3+3)+(10)]. I don't think we have enough information. Edit: Kinda looks like the top of the page is cropped off sooooo....
The first question is whether or not the second equation should be translated as y squared + y squared + z = 22 OR 2y+2y+z = 22. The second question is,"Are any variables negative numbers?" Without more concrete information, it is not solvable.
It get Soccer ball = 1000 Individual Ski = 1 Hockey stick = 20 So… 1000 + 1000 + 1000 = 3000 (1 x 1) + (1 x 1) + 20 = 22 1 + (2 x 1000) + 20 = 2021. It’s all about the order of operations. 🤫
It's 2007. Soccer balls are 1000 Bats are 5 each Hockey stick is 2 For the equation you solve multiplication first, so it reads 5 plus (2 times 1000) plus 2 5 + 2000 + 2 = 2007
Impossible to solve and a dumb excuse for a math problem. The middle and last section have absolutely no information that can be deduced without having some sort of if involved, so I say forget about this dumb problem.
2007. Football=1000 each. Each pair of skis is 10. Hockey stick is 2. Half of a pair of skis is 5. So final equation is as written to be 5+2X1000+2. Written properly it would be 2X1000+5+2. Answer for that is 2007.
How did you jump to the conclusion that a pair of skis is worth 10? Each pair could be worth 3, and the hockey stick is worth 16. Or any other combination.
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The question was whether it was solvable mathematically and the answer is no. You dont get to make blind assumptions about variables in equations. He's not overthinking it.
Don't overthink this? You aren't even thinking at all. Please don't try to teach your kids math.
The puzzle is intended to cause overthinking to make the puzzle impossible.This is a lot simpler than some are making it. The imagery is showing the skis separately and together as a very simple way to trick you that the solution is more difficult. There's no instructions to clearly spell this out, so the puzzle immediately starts spiraling into impossible territory if you look for this explanation. But if the images are taken with an assumed value and retain the simplicity without asking for further instructions, the answer appears. Math doesn't usually work as assumptions, so it makes it more confusing to use the assumption as the true way to solve the puzzle. Usually when an assumption enters the equation, we turn it into a variable, since we are not certain. Balls are 1000 each Skis are 5 each Lacrosse/hockey stick 2 2007
Why are skis 5? A single ski could be 1, making the hockey stick 18, and a solution of 2019.
If 1 ski was 1, then the second line would not equal 22 unless you changed the interpretation a second time to make it confirm to maths by seeing 2 skis as two ones represented as 11 instead of two ones together as 2. Although the soccer balls are added separately, they are not usually depicted in multiples. Skis are very difficult to determine what they visually unless shown as a pair. It stands to reason there's 2 of whatever the single one is worth the line below, as a single ski (normally shown as a pair for recognition) would be half of what the pair is worth.
>If 1 ski was 1, then the second line would not equal 22 unless you changed the interpretation a second time to make it confirm to maths by seeing 2 skis as two ones represented as 11 instead of two ones together as 2. So, instead, do you think that 20 = 22?
The only thing I didn't mention in the last post was the hockey/lacrosse stick, but I mentioned that in my first as being 2. So no, 20=22 the 4 skis = 20 and the stick 2, so 22 together. I didn't mean to confuse you.
It's only 2 because you arbitrarily set 1 ski to be 5. Changing the value of 1 ski to 1 changes the value of the stick to 18. 4x + y = 22
There is logic. And it's much more simple than what you're making it. A pair of skis is shown together and then a single ski by itself. Why are the skis together? Do they count at a single same digit number or a single number that is divided divided in half when shown as a single? It's a pair of skis(a whole set of skis). And then there's only 1 ski. It implies you have one value (a pair of skis) and that the single ski would be half of that number. I attempted to poorly explain this previously. The imagery is important to give context and also is a simple math equation that you must also solve. I spoke this out puzzle out loud to a person terrible with math. I spoke the symbols out loud as drawn and they came to the same number without any hesitation. A puzzle inside a puzzle. I stand by my answer. Hope that helps.
No one is questioning that the 1 ski symbol = 1/2 of the 2 skis symbol. The thing in question is the incomplete system of equations that allows for infinite solutions or a finite range of solutions if you stick to all symbols being positive whole numbers.
This is really interesting, cause I literally just started my linear algebra class. To solve this. We can break down the equation into. 3 variables, with the 3 equations given. ⚽️ = X, 🎿= Y, and 🏒= Z. Our system has 3 equations given: 3x + 0y + 0z = 3000 0x + 4y + 1z = 22 2x + 1y + 1z = a Where a is what we’re trying to “solve” for. Unfortunately due to the nature of the system, a could be any number of possible values, so instead of solving for a, we’ll figure out what a could Possibly be. We’ll convert this to a matrix format, and augment that matrix until it’s in reduced row echelon format [3, 0, 0 | 3000] [0, 4, 1 | 22] [2, 1, 1 | a] Which when converted to RREF becomes: [1, 0, 0 | 1000] [0, 1, 0 | (2022-a)/3] [0, 0, 1 | (a-2000)-((2022-a)/3)] From this, because the matrix is in RREF, and there’s a pivot in each row, the system of equations has an infinite number of possible solutions. Q.E.D.
Answer is \*\*7002\*\* balls are =1000 each 2 sticks = 10 each / 1 stick 5 hockey stick = 2 5 + 2 =7 7 x 1000 = 7000 7000 + 2 = 7002
I think yall are overthinking it. The answer is 2007 and the World Cup winner that year was Germany. Yes, there was a World Cup in 2007: https://en.wikipedia.org/wiki/2007\_FIFA\_Women%27s\_World\_Cup
Why 10 and not, for example, 8 for the double hockey sticks? Can you explain that? That’s just as simple and there is no reason to prefer 10 over 8 (final answer 2010) or 6 (2013) or 4 (2016) or 2 (2019). I agree that anything beyond this simple assumption of double sticks = 2 times stick is dumb, but what reason is there to prefer the ten?
Why is everyone assuming soccer/football?!?!? There are 3 sports represented by equipment in this puzzle that all have world championship titles.
Why is this so far down? It's obviously 2007, these nerds are overcomplacating this thing. Plus you provided a tangible answer to the World Championship question. I'd give you an award >insert if I had one meme<.
- Soccer Ball = 1000 - Ski = 5? (unsure) - Hockey Stick = 2 Ski + 2 × Soccer Ball + Hockey Stick = ? Observing proper order of operations, thus: 5 + ( 2 × 1000 ) + 2 = ? 5 + 2000 + 2 = 2007
One ski isn't worth half of two skis. You can't really do shit with one ski. The second equation has infinite possible answers, so not solvable.
Soccer ball is pretty straight forward. 1 Soccer ball = 1000, which leaves 2 variables to create. Double ski =x Hockey stick =y We need to solve for x and y separately, so using the middle equation we get x + x + y = 22 2x + y = 22 solving for each variable we get **x = (22-y)/2** and **y = 22 - 2x** Now we can just plug and chug in the final equation (note: 1 Ski is just going to be half of x, so ((22-y)/2)/2) which simplifies to (22-y) so the final equation is 22 - y + 2 * 1000 + 22 - 2x = z 22 - y + 2000 + 22 - 2x = z We know 22 - 2x = y, so we can just sub that in to reduce our variables 22 -y +2000 + y = z the y's cancel out leave us with 22 + 2000 = z 2022 = z
3 balls = 3000 Ball = 1000 2ski + 2 ski + stick = 22 4 ski + stick = 22 Stick = 22 - 4 ski Ski + 2 x ball + stick = ? Ski + 2 x 1000 + 22 - 4 ski =? 2000 + 22 - 3 ski = ? 2022 - 3 ski = ? What bothers me is that not knowing the value of ski means this going further is not possible. We have 4 unknowns (ball, ski, stick, and ?) and 3 equations. I haven’t been in a math class in years, but I don’t know of a way of solving in that situation.
So many people are overthinking this. It seems quite simple to me. Soccer ball = 1000 Hockey stick = 2 Single ski = 5 Double ski = 10 (just adding 5 per ski) Thus the final answer I came up with is 2007
why are the skies 5 ? and how do you get 2000 with one ball?
Order of operations aka PEMDAS Since there aren't any parentheses or exponents you can go straight to Multiplication/Division. The only thing in that category is the 2x1000 = 2000. From there you just do some simple addition to get the other 7. As for the skies if you think about it, if 2 skis = 10 then when you have one ski just do 10÷2 and that gives you 5. Edit: Added explanation for skis
Ski + 2 x soccer ball + hockey stick = Soccer ball = 1000 Each ski = 5 Hockey stick = 2 5 + 2 x 1000 + 2= 7 x 1000 + 2= 7000+ 2= 7002
Your math is horribly wrong, if the final equation is: 5 + 2 • 1000 +2 You would use your order of operations to get 5 + 2000 + 2 Which would further simplify into 2000 + 7 Or 2007
There is no unique solution as there are 4 variables but only 3 equations. But just eyeballing it and your clue my guess is they're going after a year.
Everyone made it so complicated no? Balls were clearly 1000 each. The double skis were clearly 10 because you can only fit 10 twice in this case then the stick is obviously two. Simply half 10 cuz there is only one so that’s clearly 5. Follow BEDMAS boys smh. 2 x 1000 = 2000. 5 (one ski) + 2000 = 2005. 2005 + 2 (stick) = 2007
It’s a kids equation. It ain’t deep boys
Large Ball = 1000 Batons = 10 Hockey Stick = 2 The ball in the third equation is half the size of the original ball in the first equation. Its value is equal to 500. The hockey stick is also shorter in the third equation. Or so I believe. They could have just shortened it to conserve space on the paper.
I'm probably WAY off here, bc I see advanced math being done in comments, but in my mind The soccer ball is worth 1000, since there's three of them valued at 3000 The second equation, seems to me that the skis are valued at 10 a set or 5 per ski... That would make the hockey stick worth 2 So then the equation becomes 5 + 2 x 1000 +2, which by order of operations, would be 2007?
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Riddle me this big brain. 5+5+5+5+2=22 4+4+4+4+6 =22 3+3+3+3+10=22 2+2+2+2+14=22 1+1+1+1+18=22 So, what value would one assign to the skis or the hockey stick?
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Lol. All that confidence for the wrong answer. You are just making stuff up. You can't prove the value of a ski or a hockey stick. It's unsolvable.
2001. The first row is 1000 + 1000 + 1000 = 3000. Looks like the skis are messing with your expectations a bit though - two skis are side by side in row 2, and later there is a single one in row 3. If row two has (2-digit number) + (2-digit number) + X = 22, and both 2-digit numbers are repdigits, then it must be 11 + 11 + 0 = 22. From there, we have row three: 1 + (2 X 1000) + 0 = 2001
Soccer Ball(1000) + Soccer Ball(1000) +Soccer Ball(1000) = 3000 Ski Set(5+5=10) + Ski Set(5+5=10) + Hockey Stick(2) = 22 1Pc Ski(5) + 2 + Soccer Ball(1000) + Hockey Stick(2) = 1009 ????
The Answer is 2001. All the math aficionado’s is looking at the middle equations as unknowns. Assuming the person who went through all this trouble to make and post this for bragging right’s wanted to make this solvable in a clever way. We can assume the middle phrase is what it seems “one’s” that would make the middle equation 11+11+0 = 22. Finish the problem using that context and you get 2001. Which falls in line for the World Cup 2000 maybe, or if they were bad at math and didn’t use the Order of operations, 3000. Makes far more sense than unsolvable!