Viral logic test from China
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- čas přidán 22. 05. 2024
- There is a clever way to solve this seemingly challenging question. What is the height of the table?
Problem adapted from
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What a coincidence! This same question was asked to me in a university entrance exam I gave today (they just changed up the names and heights of the objects) and I had watched this video like 3 yrs ago, so I didn't exactly remember the method, but after reading the question, the solution just popped into my mind and I solved it in a minute! Now I can know for sure that I did the right thing! :)
i..... isnt this supposed to be elementary school math?
The answer in China is the same for both one of your meals has escaped!
University entrance exam? Isn't this just a basic simultaneous equation
I felt too proud of my self solving elementary school math questions
If there were a candy reward and I'd solved this faster than the kid... I definitely would have considered keeping it for myself.
Me too
@@rcb3921 imagine
Every 10 questions=1 girlfriend 🗿
@@Anywaytimetorecord0. imaginary or real?
@@aaaaaattttttt5596 for motivational purpose take it seriously 🗿🗿🗿.
maybe you will not get a gf but you will able to become Einstein.
Solved using algebra. Going in I thought it was going to be impossible because of the three variables but was quickly surprised with how well it worked out.
As soon as you spot the trick that the combined height of the cat and the turtle is in fact one variable, it becomes quite easy.
But its for elementary school 😭
It's just 1 variable, but with extra steps
The moment I saw 2 variables cancel each other, I can't help but "Bruh".
there is no variable in the problem. each item is a fixed measurement. you used elimination and substitution to reduce the three measurements down to one.
I love that some of your videos are simple while others counterintuitive. It forces me to remain critical even when I the answer appears simple.
Never going to China, I'm too short to sit at a table of 150cm.
A 150cm table has nothing to do with China
@@user-bb7ic8kw1r I'm not taking any chances.
What if its not table but cat's tree?
Yes mee too
LOL, I recognized your name. Funny you follow this channel too :D
I figured it out and even found both methods! The problem is that I am no longer an elementary school student...
Rico Sanchez same here😅😅
Me too
Now. Let's calculate the volume of air(20%O2) necessary for burning 200g C2H6O (70% pure) under the conditions of 2 atmospheres and 30°C.
@@saecsee on it. Class 10 reporting here.
same and irony is i teach in one...
As a construction electrician, I have a lot of measurement shorthands I know work but have forgotten the principles behind. I knew averaging the heights would remove the cat and turtle as variables, but didn't immediately know why until I saw your visualization.
That's what I did. I averaged them out, and then proof'ed my answer with the visual approach. Idk, why I didn't immediately think about making it an equation.
@@christophsiebert1213 I've run into lots of people who like to turn everything into equations lately. Especially younger people. I'm curious if that's how they teach now. I went up to calc 2, but my first approach is to still just recognize ratios or other relationships between numbers and plug the numbers in that way. I save equations for when things get more complex.
@@ElNerdoLoco I mean, equations ARE the language to calculate in. If we just go by eye and ratio, we can make errors. Even if slightly, those errors get propagated through the system and get bigger. So, working with equations from the outset, that you know how to use, should be the way to go, imo.
But of course, this is for the real serious stuff out there. For something silly and fun like this here, you can go whichever way works, as long as you can proof the result with a separate method, best case an equation.
I got teached calculus by learning ratios visually and later on got more and more equations. And I think that's right. We should just not forget that one can start off solving problems more simple and comfortable.
Yeah, as a mechanical engineer I looked at it, and did the same thing. But I didn't have a lot of confidence in my answer at first.
I went about this the other way: I formed the equation, noticed that the solution was the average of the two, and tested with other heights to make sure it wasn't a fluke.
The most difficult part about this puzzle is figuring out what such a high table could be useful for.
Edit: They make standing desks that big, I looked it up.
Must b e a standing desk.
@@thassalantekreskel5742 150 cm is a lot even for a standing desk. Many people are shorter than that and wouldn't even see what's on it.
I'm American, so I am just blissfully unaware :)
@@Roonasaur 150 cm is about 5 feet.
@@crowbar_the_rogue TY. :)
(I could've googled it if I really cared, lol, but thank you)
Presh, I’m just a Dad of two Primary School boys. Twice a week I take you problems to the school and we solve them with the kids who love maths. So in regional Australia you are inspiring kids to love maths more!
Good for you. (I mean that genuinely.)
^Pin this Presh
great!
I love maths too
Paul Kennedy have you ever been used Brilliant?
As an engineer, I'm glad to know that my manual algebra skills are still intact.
Q: How do you know somebody is an engineer? A: Wait 5 minutes and they'll tell you.
@@madcowusa4277 That’s a fair observation, not gonna lie
same lol
With T = height of table, C = height of cat, and S = height of snapping turtle:
1) T + C - S = 170
2) T - C + S = 130
Subtract 2) from 1)
3) 2C - 2S = 40 or C - S = 20
Substituting 3) in 1)
T + 20 = 170 so T = 150
C can be any height as long as it is 20 cm taller than S. The key is that you are solving for T and (C-S). Two equations and two unknowns.
Of course, rewriting 2) as T - (C - S) = 130 and substituting will give same result.
Why does the hamburger have legs?
r/cursedcomments
I'm laughing
To be able to jump off the table to switch places with the cat.
Because it is a Cheespider
To keep his pants up.
Thank you for 1.1 million views! Happy 1 year anniversary!
I love when you say "Did you figure it out?"😂
Anyway, I solved it! Thank you!
can u figure out what ln (-1):i is?
Could you please tell me, how tall is the cat and tortoise
I didi that.. The second way is 😎cool
What is the height of cat and Turtle
I did it differently. The difference between both heights was 40cm, which told me the cat must have been 20cm taller than the turtle, thereby resulting in an addition or subtraction of 20cm from the height of the table, which told me the table was 150cm. I take tremendous pride in the fact that the answer came to me in what felt like 10 seconds, maybe 15, but certainly under 30.
Well it's not really an answer but an arbitrary decision. The cat could be even 22.5cm taller, who says it's 20 besides you?
That's how I did it too.
@@kirakira9906 I used the same method he did. The total height with the cat on top is 170, the total height with the turtle on top is 130. This is a difference of 40. The Average Difference in Distance is 20. (A+B)/2 = C is an average distance and it is relative. Here we have 20 as the relative average difference in distance. Then we can use that average distance in height to determine the height of the table by either combined heights simply by subtracting from the taller height or adding to the shorter height seen by these to equations: 170 - 20 = 150 or 130 + 20 = 150. This is equivalent to the algebra method by taking a + b - c = 170 and adding that to c + b - a = 130. Adding the two equations cancels out both a and c leaving 2*b = 300 resulting in b = 150. It's the same deduction just a different processing of achieving it. In many cases there are multiple algorithms to solve each problem.
@@kirakira9906 No, it must be 20cm. 150 + cat - turtle = 170. Therefore, subtracting 150 from both sides yields the equation cat - turtle = 20cm.
@@kirakira9906 If you subtract the equations you get Table-Table-Turtle-Turtle+Cat+Cat=2*Cat-2*Turtle=40 cm
Then you divide by 2 on both sides
1/2(2*Cat-2*Turtle)=40/2=Cat-Turtle=20 cm
Therefore Table+Turtle-Turtle-Cat+Cat=Table=170-20=150 cm
I initially solved it by using algebra (too quick!), but then I came up with a different visual solution, this one based on subtraction: You can see that when you go from the first drawing to the second, the bottom of the bracket gets higher by the difference between the turtle and the cat. The top of the bracket also gets lower by the difference between the cat and the turtle.. Because of this, the difference between the two brackets is two times the difference between the turtle and the cat. Since the difference is 40 (170-130=40), the difference between the heights of the turtle and the cat must be 20. That means if we replaced the cat with another turtle in the first drawing (so that there were two turtles instead of a turtle and a cat), the measured height would be 150 instead of 170. Of course, the difference in height between the turtle on the table and the turtle on the floor is just the height of the table, since those turtles are both the same height if not for the table!
I am glad to see that I was not the only one that utilized this same visual solution using subtraction!
I mean, this is literally algebra too xd It's just a different solution to the same system of equations.
Good logic
I solved using logic but, accidentally, used algebra. I thought that the difference was 40cm, so the cat must be 20cm taller than the turtle(because the 130cm on the second picture it is due to a 20cm taller from the bottom and ends 20cm higher too, 40cm in total). Then I figured, if we put a cat at the bottom and a cat on top, the difference between their heads will be the tables height. Resulting in 150cm(170cm-20cm when replacing the turtle's height and likewise in the second picture). I dont know if I explained myself, but I'm happy I figured it out.
I (almost) accidentally found the answer xD Wrote the problem down, and tried to add (x + c - t = 170) to (x - c + t = 130) which got me a 2x = 300 => x = 150. But doing that wasn't my original plan... just something I decided to do after writing it down.
x+y-z is 170
x-y+z is 130
Therefore, 2x is 300 and x is 150
Algebra rocks 😅
Same here
I knew that.... I just didn't want to say anything.
*Then says it anyway
I wonder why? HMMMMMMMM
How did you combine the two equations
@@samuelasamoahboateng4306 since there are 3 variables and 2 equations you can take one of the value as 0. Eg take z as 0 then 2x=300 , hence x=150
Given the swapping of variables for each example, I knew the answer would be in the middle of 130 and 170, so 150. The hard part was figuring out how to prove that it was.
Exactly my situation, I can find the solution easily in my head, proving it for me is like trying to calculate a new digit for pi
You could have just add 130+170 and devide it by 2. Your result is an average height which is also a correct answer.
That's what happened to me too. The correct answer jumped out as the average between the two, but I felt the urge to prove it algebraically and get Cat Height in the form Turtle Height + Height Difference so I could do the problem after having proven it.
Oh I solved using systems of equations: (t = table c = cat r = turtle (r is for reptile but I already used t))
r + t - c = 130
c + t - r = 170
Using algebra, we can see that the difference in height caused by switching the turtle and cat is 40 cm, and half that height will come from the added height of the cat, the other half from the subtracted height of the turtle, so the difference in height from the turtle to the cat is 20 cm. Therefore c - r = 20.
This can be rearranged to c = r + 20
Substitute: (r + 20) + t - r = 170
r's cancel, 20 + t = 170 --> t = 150
The table is 150 cm tall.
I did this one two also.
But my other method was made without any calculations in my head. Just put both pictures on top of each other (x2). You get 2x table - cat + cat - turtle + turtle=300. So 2x table = 300. 1x table = 150.
Edit: hahahhaha... and its the first solution in video.
I really like this one. I used a visual method as well but just treated the turtle height as "0". Then the 2 equations are table + cat = 170, table - cat = 130. Got the same answer that way
That's a really clever trick. 'Let [variable] = 0' is a typical mathematical technique, but it's not necessarily intuitive to imagine a turtle of zero height
Great video! The second visual explanation help me finally understand the logic of adding two equations to find the value of a variable.
I think I found my doppelgänger
It’s interesting because the visual one at the end was actually the same as the algebraic equation method
y know when I looked at this problem I immediately thought this was gonna be easy but and it was, however after realizing that the stuff that I learned in high school is being taught to elementary school students in china, it expanded my views on the world. this was very enlightening
I got perfect scores in Canada-wide math contests back in high school and consistently scored top 50 in the country for my grade.
If I went back to China, I'd be a below-average math student. And not just slightly below average, I'd be one of the worst in the class.
India too. They do advanced maths years before we do in Australia
I learned how to tie my shoes in elementary
I don't know how to tie shoes in high school
@@suryanshsingh4533 true . Me too.
Same😂😂
What I did was that when going from 170 to 130, you shorten this distance by (cat-turtle) on both sides. Therefore 2*(cat-turtle) = 40, therefore difference between height of cat and turtle is 20. From the second picture, if we now put a cat on a table instead of turtle, we know it will be 20cm higher = 150 cm. Then we can move it all down one cat, and see that it's the height of the table.
Did the same thing almost. I used algebra to solve for the height of cat/Turtle
Yep this is pretty much what I did.
The fact that the same subjects appear in both situations, and in each case they swapped places in a 1 for 1 matter, means that you can use the mean equation to figure it out. Which might be closer to the second method. But it takes less time to calculate, than the time given by the "pause the video" phrase...
The way I solved it was a little different. I noticed that when the turtle and the cat are switched, the height between them changes. Using the first image as a reference, the height between the cat and the turtle in the second image decreases on the top and bottom by the difference of the heights of the cat and the turtle. Using this, we can deduce that 130cm plus two times the difference of the cat (which I'll call "c") and the turtle (which I'll call "t") equals 170cm. Written better like this: 130+2(c-t)=170. Simplifying, we get c-t=20. The difference of the heights of the cat and the turtle is 20cm. After this, I took the second image and wrote it for the height of the table (which I'll call "T"), which turned out like this: T=130+c-t. We've already established that c-t=20, so substituting it in gets T=130+20, which is 150. The height of the table is 150cm. Christ that took way too long to write 😑
Yes it's interesting that you can find the difference between the cat's height and the turtle's is 20cm, but you can't solve for their heights beyond that. The turtle could be literally any height, one centimetre, a mile, and the result for the table would still be the same. It frustrates mathematical thinkers because they immediately see it's impossible to solve for the whole system as you usually would, but there's still an answer for the quantity requested
Here's another solution.
Let x be the difference between the height of the cat and the height of the turtle.
In the first picture if you replace the cat with a turtle or the turtle with a cat, the distance will be reduced by x.
Replacing both animals will reduce the distance by 2x.
Therefore 2x = 170-130 x = 20
Now you can either add x to the second picture or subtract x from the first one to get the height of the table.
Im also using that method, but in algebra
A(table)+C(at)-T(urtle) =170
A(table)+T(urtle)-C(at) =130
___________________________ -
C-T-T+C =40
2C-2T = 40
2(C-T) = 40
C-T = 20
________
A+C-T=170
A+20=170
A=170-20
A=150
I assume you have to use elementary level math, or else is kinda cheating...
@@aifesolenopsisgomez605 that is elementary level math. if a child got a good understanding for math these basic algebraic equations shouldnt be a problem for it.
too convoluted answer, way more simple than this.
Great explanation.
Simple and concise
I started solving with algebra, then i figured out a simplier and quicker solution with logic:
Top turtle to top cat = 170
Top cat to top turtle = 130
The difference is based on the height of the cat: it's taller than the turtle by 40/2 (caused 1x its tallness is subtracted when switching cat with turtle on top of the table; another 1x is subtracted when switching the turtle with the cat on the bottom of the table), so the height from turtle to turtle should be 170-20=150, but it's the same as floor to top table height
i dont know what i did but I believe this comment sums up how I got there haha
It is not 150cm. It is 170cm. The cat has 70cm and the turtle 30cm.170cm - 100cm = 70cm. 130cm - 100cm = 30cm. 200cm - 30cm =170cm. The table is 170cm high.
@@robertzappe9747 that's impossible, 'cause top turtle to top cat is 170 cm and the turtle and the cat are not of the sane height (otherwise top cato to top turtle should be 170 cm too, but instead it is 130 cm).
First one of these I've properly figured out! All it took was a VCE Maths Methods level of learning for an elementary problem lol
Made a lot of algebraic mess and still couldn’t come up with a proper answer. I started with Cat + Table - Turtle = 170 - (Cat - Table + Turtle = 130). It ended up giving me cat’s height as 150😂. But after reading comments, I went back, and solved that the cat is 30, turtle is 10, and the table obviously is 150.
Actually there isn’t enough information to calculate the cat’s or turtle’s heights. We know that the cat is 20 cm taller than the turtle, but that could mean that the turtle is 10 cm tall and the cat is 30 cm tall, as you stated, or the turtle could be 15 cm tall and the cat 35 cm tall. And although it’s far fetched, it works out mathematically for the turtle to be 500 cm tall if the cat is 520 cm tall.
I feel like im Einstein when my answers was right :D
Ikr
@@anshumanagrawal346 ikr mtlb
@@critisizerr245 I Know Right
Yes
I used the simultaneous equations method with the thumbnail and was feeling pretty good that I remembered how to do that 20 years after studying it in school. Then I watched the video and you took the wind right out of my sails by saying kids in China do this in elementary school! I was about 15 when we studied simultaneous equations at school. I could never have solved this in elementary school ha ha! The visual proof was cool too. It didn't occur to me and it's quite pretty.
I didn’t even think of trying to solve it with an equation even though it makes perfect sense to do so.
I just tried to solve it the visual way and eventually realised I might have to stack the tables. When I did the solution suddenly became clear.
This is also a great question for algebra class. intuitively I knew somehow they must be able to cancel each other but my math brain is too rusty to instantly tell how exactly, so I drew the other half below the right figure, just the opposite of the video, and then I see it right away, it's a good way to understand the tricks we use in systems of equations.
I rearranged the second equation so it gives the height of the turtle and substituted it in the first.
That worked, too, but adding them is probably a lot easier :D
How did you do that?
I did the same.
@@kirakira9906 probably something like
{cat + table - turtle = 170; table + turtle - cat = 130} |
2 > turtle = 130 + cat - table ->
1 > cat + table - (130 + cat - table) = 170 -> cat + table - 130 - cat + table = 170 -> table + table = 170 + 130, so table is 150
1:51 *Now notice the height from the top of the cat at the botten to the top of the cat at the top*
This is so catchy!
By using algebra by adding the two and taking the average is one way of solving it. The method I used was similar but with a slightly different variation. The two heights being 170 and 130 respectively have a difference of 40 in height. Dividing 40 by 2 gives 20. Then you could either add 20 to the shorter height or subtract 20 from the taller height both giving a result of 150 in height.
An interesting way of solving this is noticing that picture 2 shows the inverse of operations imposed on image 1. So you can just find the average height of the two:
(170 + 130) / 2 = 150cm
This abstracts away the algebra involved so no cancelling of terms is necessary.
I dont know why i found it so funny when he said "now we can erase the animals from the picture".
You must be very careful how you do that. If you erase the cat, the turtle will have a height of -20.
David Hardy Yes, because he removes himself from normal imagination into rigid, mathematical operations mode.
LMAO
Solved it by trial and re-try. Tested for different heights of animals and eventually found that the animals' heights must differ by 20cm. From there the only fitting height of the table was 150cm.
I got it pretty quickly by arranging method 1 in a certain way. Two equations in the form x+y=a, x-y=b. In this case:
Table + (Cat - Turtle) = 170
Table - (Cat - Turtle) = 130
Which shows that Table is directly between 130 and 170, so it's 150.
I did it a different visual way and got a different answer. In the first picture it shows 170cm being from the top of the turtle to the top of the cat. That means that the 170cm doesn’t include the turtle’s height and includes the cat’s full height. Then in the second picture it shows the cat on the bottom and the turtle on top with the 130cm not including the cat’s height and fully including the turtle’s height. If you then make the second picture fully include the cat’s height and not include the turtle’s height like is shown in the first picture the 170cm would then go from the bottom of the cat to the bottom of the turtle which is just from the bottom of the table to the top of the table. Therefore the table is 170cm.
A simpler visual method. Imagine both cat and turtle are the same height. Then both measurements will be the same, and will each be the height of the table. Now imagine the cat grows a bit taller. One measurement will increase by some amount, but the other will decrease by exactly the same amount. So the average of the two measurements will not change and will remain equal to the height of the table. Therefore the height of the table is the average of the two measurements.
This comment is underrated
Indeed, this is illustrated by the addition of the two equations.
@@tibfulv Yes, but it's a bit more intuitive = more suitable for youngsters. If I had been forced to solve this problem with a pen and paper, I would have used the set of equations method, but since I wanted to solve it in my head, taking the average seemed to be the obvious way.
Can u show it through equations
Wow !!! Same thinking bro !👌👌
2:09 yes I can VERY CLEARLY VISUALISE THIS
Even if you forgot your algebra, by giving values to each item, calculating the distance in each scenario, you can fairly quickly see the solution is to add them together and divide by 2.
I didn’t use any of those methods and still got it. Here’s my thought process: the turtle and the cat simply switched places, so half of the difference between 170 and 130 would be the difference between the two, which is 20 cm, then we take the top turtle (130-20=110) and add two turtles to substitute the cat (110+2x20=150) and that would be the height of the table
Sameee
Same - the cat is 20 cm taller than the turtle, so the height of the table is either 20 cm shorter than 170, or 20 cm taller than 130, both of which adds to 150
@@aliquida7132 Not necessarily. The cat could be 30 cm tall and the turtle could be 10 centimeters tall and this would still give 150 for the table. The cat could 32 cm tall and the turtle could be 8 cm tall Why do both cases work? The height of the cat and turtles are unknown and they are relative. What is known is that the difference between the two stacked heights including the unknown height of the table is 40 cm and since there are two variants, the Average Difference In Distance between the two is 20. You can either subtract the this average difference in distance from the taller height or add it to the shorter height and both will give a result of 150 cm which is the height of the table.
@@skilz8098 You're right about the general logic here! You've got one trivial error that threw me off in trying to understand what you were saying, though-if the cat is 32 cm tall, the turtle is 12 cm tall, not 8 cm. The numbers you used are ones that sum to 40, not ones with a difference of 20.
But yeah, for all we know the cat is 350 cm and the turtle is 330 cm. Or maybe the cat is 6 cm and the turtle warps reality to be -14 cm. All we can figure out from the given information is that the values differ by 20, so we can't rule out even extremes like these. And if you plug these values into the equations, the solution still works :D
Is it bad that I figured out the height of the table by comparing both measurements and coming to the conclusion the table was a bit smaller than the first one by roughly 20 centimetres ?
I wrote out both equations, but I ddin't add them.
I disregarded the table as the common element in each equation. That showed me that the difference between cat-minus-tortoise and tortoise-minus-cat was 40. Given that the differences had to be symmetrical they had to be 20 and -20.
So the height of the table was 170 minus 20 and also 130 plus 20.
(Cleverer or more practised people than me would have been able to think through this almost instantly of course.)
that exactly what I did
Yeaa I was thinking it's something along the lines of a system of equations but that's something I need to review for the sat too
Very good description. May I use your photo for this question with reference to your channel in my school?
amazing puzzle and very easy solution...
I used the algebra method, but decided to add 40 to the table with the turtle on top, to equate the two figures. I then defined cats in terms of turtles, and decided that the cat was 20 taller than the turtle. Using this knowledge, I replaced all cats with turtles, and then all turtles cancelled out.
This is why math is fun. Many ways to get an answer.
For the first one I did,
T=turtle and c=cat
T+ 170 -c,
And C+ 130-t
Change to
2t+40= 2c
Divide on both side
T+ 20= c
Change all the cats in the original equation to t+20
And simplify
aaaa my math teacher gave this problem as homework, i noticed your channel icon on the bottom left!!!! thank god i know this channel
This is interesting because we appear to have two equations in three unknowns, which usually we would consider not solvable. When I first glanced at the thumbnail, my mind said, both at the same time, "That's unsolvable. That's easy." ;-)
The diagram method is exactly the same as the algebra method. It is like using rulers to add numbers. The animals should not be taken away before moving the bracket, though. It is clearer if the upper leg and the lower leg of the bracket are both moved down by one cat height. It can also be done the other way, with the turtle on the top of the upper diagram and the bottom of the lower diagram, and move the bracket down by one turtle height. This corresponds to summing the equations in the reverse order. It also gives a hint into why this is not two equations in three variables. The height of the cat and turtle do not matter, as long as they differ by 20, they can be anything. We are not trying to solve for three unknowns. Two of them are still variables. If we had additional information about the height of the cat and the height of the turtle, like their sum or product, we could solve for those heights as well.
Let me show one way to visualize why we can know the third variable that you may not have thought about yet.
We have 3 equations so lets think of a 3 dimensional room. We have a x,y and z axis. Each of those represents one of our 3 variables. Each solution is a ordered number triple (x,y,z) which means that each point in our room is a possible solution.
Now we introduce our first equation. We can think of this equation as a plain. Only points on this plain satisfy the equation. Our second equation is another plain. As long as our two plains are not parallel they will cut each other in a line. Only points on this line satisfy both equations.
This line can have the property that it is in a 90 degree angle to one axis. In that case the value of the variable associated with this axis is the same for all points. This means that there is only one solution to this variable. This is exactly the case in our problem.
Visualization is a good idea.
We already know what the graphical solution looks like; it is a line perpendicular with the table axis at a value of 150 and which projects into the cat, turtle plane as a line which intercepts the cat axis at 20 and the turtle axis at -20. We can see this as the intersection of two planes; first the plane perpendicular to the table axis at 150 and second, the plane perpendicular to the cat, turtle plane through the projected line in the cat, turtle plane just described.
The described solution line has one value for the table height and an infinite number of values for each of the cat and turtle heights.
This isn't exactly what you described, you described it with two different planes. Following your original thought, the two intersecting planes may be described more particularly as follows. Both planes contain the solution line described above. The plane corresponding to the first equation passes through the cat, turtle plane, where the height of the table is zero, on the line which has cat intercept 170 and turtle intercept -170. The second plane passes through a line in the cat, turtle plane on the line which has cat intercept -130 and turtle intercept 130. These two lines are on opposite sides of the origin, they are parallel and the corresponding planes lean toward each other to intersect on the solution line described above.
Either of these pairs of intersecting planes is a strong visualization of how there is one solution for the height of the table, but an infinite number of solutions for the cat and turtle heights.
@aeromodeller 1 I am also fascinated that "There exist some 3 variable problems with 2 equations, whose exact answer/value can be found for 1 variable." That's something NEW to me!
Like you, I previously believed that you can either solve for all 3 variables IF AND ONLY IF you have 3 linearly independent equations, or none at all if you have less than 3 equations. This problem proves it wrong.
I can see now after having thought about it why this problem is solvable for Table. Because by chance it is a 2 variable - 2 equations for Table, if you make the equations like this:
Table + (Cat - Turtle) = 170
Table - (Cat - Turtle) = 130
If we rename (Cat - Turtle) as DIFF ... the difference in height btw Cat and Turtle
Table + DIFF = 170
Table - DIFF = 130
This is a 2 eq - 2 var problem. Both Table and DIFF are solvable to be
Table = 150
DIFF = 20 = Cat-Turtle
@Random Person
Your explanation is quite useful. I've never thought of it as "the answer line is in 90 degree angle to one axis.", though.
I would just describe the answer line as a line in 3 dimensional (x,y,z) space, whose coordinates satisfy the following line equation:
y - x = 20, z = 150
Essentially and visually, it is a line y = x + 20 in 2 dimensions, flat x-y plane, floating at the z - height held constant at 150.
Table = 150
DIFF = 20 = Cat-Turtle
and
y - x = 20, z = 150
are different forms of the two equations that correspond to one of the pairs of intersecting planes that determine the solution line; first the plane perpendicular to the table axis at 150 and second, the plane perpendicular to the cat, turtle plane through the projected line in the cat, turtle plane. Both of these equations in this problem contain all three variables, sometimes hidden.
Cat - Turtle + 0 x Table = 20 contains Table multiplied by zero, so all values of Table satisfy this equation. When Table = 0, this plots in the Cat, Turtle plane as the line with Cat intercept 20 and Turtle intercept -20. This same line is valid at every value of Table, so this equation represents the plane which is perpendicular to the Cat, Turtle plane through the projected line in the Cat, Turtle plane.
Similarly, Table + 0 x Cat + 0 x Turtle = 150 is satisfied by all values of Cat, Turtle, but only one value of Table. This is the plane that is perpendicular to the Table axis at 150.
The intersection of these two planes is our solution line, in which Table = 150 and Cat - Turtle = 20.
It is interesting that we have two sets of equations and two corresponding sets of intersecting planes producing the same solution line.
In Singapore schools, pupils use *bar drawing* method. This is a simple one, even for kids.
Yay models yay
How this method works? Measure using a scale bar?
Nobody said it was hard. And education in singapore is very stress
My brain must function weirdly. I solved this by first finding the height difference between the cat and the turtle, which is half the overall height difference. I got a 20 cm height difference. I used that to calculate the distance between head tops if it were two turtles by adding 20 cm to the distance if the turtle is on the table and the cat is on the floor. I got the correct answer of 150 cm.
As linear algebra student I had some difficult to understand how could solution be possible even if the linear equation were just 2 instead 3, having 3 variables, but then I've realized that this problem has infinite solution because, even if the high of the table is a constant value of 150 cm, the high of the turtle depends by the high of cat or vice versa, according to the rouche capelli theorem.
And that explain why some people have found the right solution even choosing an arbitrary high for the cat or for the turtle.
I did it visually but thinking like: 170cm had the same size of the 130 + cat, so the cat is 40. Then I made this equation: 170 - cat + turtle = 130 - turtle + cat, and so figure out that turtle = 20. Finally, I just did the equation’s sides and both were 150
Nice... It is Same with this.. You can eliminate, where h= table...
h= 170-cat+turtle
h= 130-turtle+cat
------------------------------+
2h=300
h=300/2
h=150
Let X = table, C = cat, and T = turtle. We have X + C = 170 + T and X + T = 130 + C. Add these two equations. Then 2X + C + T = 170 + T + 130 + C. Then 2X = 300. Then X = 150.
I think this is a correkt answer
I did the same
That's what he did..?
I had the same exact variables and same exact set up lol.
@@T3tr4gr4mm4t0n Because of the equivalence relations. If a=b, adding a to bothe sides is the same as adding a on one side and b on the other.
I figured it out via a slightly different method before watching. I noticed that the cat and turtle swapped around in both scenarios meaning their heights weren't important. Then I figured it was simply the halfway point between the two heights. 150cm. The algebraic way makes much sense and in a way I guess I did that without realising it!
I've seen only preview, but the answer is 150cm
a - table, b-cat, c-turtle
a+b-c=170
a-b+c=130
If we will sum the parts we will get
2a=300
a=150
I got stuck just solving for the cat and the turtle, when I only needed to figure out the height of the table
You can also find cat and turtle height
@@miyaj6104 how please
There are no fixed heights for them. They are whatever that fits with cat - turtle = 20. It could be 60 and 40, or 30 and 10, etc
As an elementary school student, I might have been challenged by this.
Two animals interchange positions depending if they were at table 1 or table 2, therefore any difference in distance between the two dimensions is obviously due to just swapping their positions therefore making the 40 cm difference between the two dimensions divisible by two (since there are two tables) in order to effectively eliminate the animals from the picture altogether. This invariably means that 20cm must be added to the shorter dimension and 20cm must be subtracted from the bigger dimension in order to arrive at the same measurement for both tables since both tables must be the same height.
The expression minus C plus T is common to each equation so it is just a case of substituting -C+T to get the answer without even needing to know what C and T are. The question doesn't ask what C and T are anyway. 150 cm.
Here's a fun little math joke I recently saw online.
Q: What do you call a number that can NOT stay still?
A: *A roamin' numeral*
:thinking:
variable
lol thats pretty good too @Amiy Kumar
Gather you things and leave the internet.
Algebra, please stop asking us to help you find your X. She has left you and is never going to return. Don't ask Y. Z?
Q: Why can't you breed a mountain climber and a mosquito?
A: Because you can't cross a vector by a scalar.
Just stack one arrangement above the other; the given dimensions will add up to give the height of two such tables stacked, giving 150 has the height of one table.
Approaching a problem visually is more satisfying than applying equations!!! 😊
EDIT: Oh, you mentioned the visual method as well in your video!!! I was not expecting this to be there!!!
Oh thank god he started out the same way I did. Sometimes he goes off on a tour through math concepts I never learned, using terms like 'simply' and 'just'.
I loved this. I was trying so badly to use the difference between the 2 images (40cm) but I couldn't think of how.
Got the right answer in a much more round-about algebraic way. I subtracted the 130 height equation from the 170 height one to remote the table height instead of spotting that things would cancel out from adding them. Got there in the end at least
As soon as I looked at the problem, my intuition told me the answer is 150.
But then I solved it slightly different.. 170-130=40. 40/2=20 you can add 20 to 130 or minus 20 from 170 and you'll get 150.
Also, the reason why I came up with this method is because mathematically the cat is taller than the turtle by 20cm so if the turtle is 10 the car is 30cm.. the difference in height is 20cm and when you flip their position the twenty doubles and thats why we have a difference of 40cm between the first and the second height.
One of the few problems of yours i solved
My sol was setting it up as an algebraic problem
using variables x,y,z to represent the cat,turtle and table respectively
x+z-y=170
y+z-x=130
adding the 2 gives 2z=300
dividing 2 from both sides gives z=150 which is the height of table
please, help me in understanding what's wrong in my reasonement:
turtle is X, cat is Y, table is Z:
so 2Z+x+y=300
That means that, if the solution of the video is right (table is 150), cat and turtle are 0 cm high.
I can't understand what's is wrong in my idea.
please, help me in understanding what's wrong in my reasonement:
turtle is X, cat is Y, table is Z:
so 2Z+x+y=300
That means that, if the solution of the video is right (table is 150), cat and turtle are 0 cm high.
I can't understand what's is wrong in my idea.
please, help me in understanding what's wrong in my reasonement:
cat is x, table is y. So x+y=170
table is y, turtle is z. So y+z = 130
so 2y+x+y is 300
But, if the solution of the video is right (table is 150), cat and turtle are both 0 cm high.
I can't understand what's is wrong in my idea. Please, help me!
This channel makes you think about how much you don't think about what you can think correctly
Damn I was trying to solve it visually when my brain went “Ah it’s probably just a visual aid for the math problem, it probably isn’t one to one with the actual scale just try the math you’re bad at instead.”
The visual method was just visual adding of the two equations in method 1
My method was simultaneous equations.
T(able)+C(at)-U(turtle)=170
T-C+U=130
Add the equations to get
2T=300, T=150
Nice one. Figured it out quickly using algebra. Would not have been able to do this in elementary school though.
To solve this, I used the Gauss Algorithme which works perfectly well with:
T -height of the Table
X -height of the Tortoise
Y -height of the Cat
By declaring:
T = 170 + X - Y
T = 130 - X + Y
Then:
170 + X - Y - T = 0 |L1
130 -X + Y -T = 0 |L2
And with L1 as a pivot and by doing:
L2 + L1 (on L2 only)
You obtain:
170 + X -Y - T = 0
300 -2T =0
So:
2T = 300 and T = 150!
That’s it!
Have a good day!
(It is allways good to look at the written calculus)
(Sry for my English)
Why keep it simple when it's also possible doing it compacted?
Maye, you must be from academia, which like to make simple things look complicated for publication purpose.
Resolving with augmented matrix, interesting
Od you can (170cm + 130cm) : 2 = 150
I just subtracted the difference between rabbit and turtle then divided by 2 and with that you get 20cm added it to the Turtle's height and got 150cm.... but that's a very well unorthodox way of doing it ..
I figured it out through pure intuition because you said it was an elementary school problem. 😆
At that point I just had to look at the elements and notice the pattern. It's asking for a specific height so the numbers are obviously the starting point. The cat and turtle swapping positions leads to the difference between the two numbers, and that is the only relationship between the numbers. That difference is 40 so add 20 to the lower number, 150.
because you only need two:
x - y = 170 cm
y - x = 130 cm
y = 130 + x
x - 130 + x = 170
x + x = 300
2x = 300
x = 150
somehow as long as 130 and 170 are added together on one side of the equation, then it will work out.
@@denusklausen3685 You should recheck your equations. If you were to substitute the x into your equation, x and y don't match up.
@@paulke1859 it does add up, 170 should be -170, but it isn't a matter of algebra but of relations. It is a problem of logic. There would be no need to show the right equation, all I am showing here is that the relation between 130 and 170 is such that it naturally suggests 150 as the answer.
I did it a different visual way. The image on the right measures the distance from the difference in height between the cat & the turtle higher at the bottom & from the difference in height between the cat & the turtle lower at the top. So the total difference in distance between the 2 images (40 cm) is double the difference in height between the 2 animals, making the cat 20cm taller than the turtle. If we swap a cat for the turtle in the other image, the distance in both images will be 150 cm. Since this distance is measured from the top of an animal on the floor to the top of the same animal on the table, the table must be 150 cm tall.
It's fun to find the "visual" solution to these types of problems and avoid using algebra whenever possible. Visually the answer came to me when I tried a trick from the solution to one of Presh's other puzzles (I won't say which one).
I used algebra but somehow took atleast 15 minutes doing the complex way
Here's how I did it:
Distance from top of Tortoise and top of Cat in the first picture is 130cm and in 2nd picture it is 170cm then height of cat is 40cm. Then from first picture height of table is 130cm + tortoise height. You can confirm this by compering the same with second picture. In the second picture height of table is also 130cm + tortoise height as the cat's height is excluded. But height of cat is 40cm, then in the 2nd pic distance from tabletop to cat top is 130cm - 40cm + tortoise height = 90cm + tortoise height.
Also in the 2ne pic, given distance is 130cm. Therefore, (90cm + tortoise height) + tortoise height = 130cm which means height of tortoise is 20 cm. Now from either pictures, adding the remaining height of the tortoise height of table is (170-40+20=)150cm in the 1st picture, and (130-20+40=)150cm.....
THANK YOU
I almost solved it visually, I thought it was 140.
It was simple enough to work out as long as you knew how to turn it into an equation, but the fact that i didn't learn how to do that until highschool is what shocks me
Chinese elementary school students are on a whole different level
I figured it by looking at the difference between the two. The difference between the cat and turtle is 40/2 (because the pictures have them switching places), which is 20. Adding 20 to the 130 in the picture with the turtle gives me 150, which is what the distance would be from the top of a turtle on the floor to the top of a turtle on the table. That would also be the distance from the top of a cat on the floor to the top of a cat on the table, or just the height of the table without animals.
My Engineer brain thought "Two Equations, 3 Unknowns, unsolvable"
I'm continually blown away how becoming smarter can make you less smart in some ways
same thought process here 😂
Yeah but you have to solve just one. And two of the “variables” are to be discarded. Be an engineer, find ways trough use looong shortcuts etc. I design roads, parking lots, storm water lines…. Not structural but still engineering.
@@mariokajin solving a system of 6 linear equations brings us height of table = 150 cm, height of turtle = 10 cm and height of a cat = 30 cm.
I solved it visually in a slightly different way: overlapping the two images clearly shows that the turtle is 20cm and cat 40cm.
Actually, the height of either animal is not able to be calculated. All that is known once the solution is found is that the cat is 20cm taller than the turtle. They cat could be 160cm tall and the turtle 140cm tall. You can't assume diagrams are to scale unless stated.
Yes but it works nonetheless. The cat must be 20cm than the turtle because from the left picture to the right one it loses 40cm because of the height difference between cat and turtle 20 twice. So the cat must be 20cm taller. Now replacing the turtle on the left picture with a cat, we have a height of 150cm, since we have to subtract the 20cm from the height difference. Now 150 is the height of the table, since both cats are equally tall and therefore can be subtracted from the equations.
At least that's how my solution was
@@thebigmacd It actually is! :) The height of the cat equals to 24,4.. and the height of the turtle equals to 4,4... To confirm: 24,4-4,4=20 170-20=150 and 130+20=150. If anybody still wants this worked out I can post it here, worked it out on paper.
also you can use the method to figure out how many centimeters = 1 pixel and the times the answer by the total pixels of the length of the table
1st noticable thing is that there is 2 numbers with 3 unknowns so if any certain solution exists then one of unknown is free to select whatever you want. Thus we can just assume turtle is zero height and solution comes obvious.. table + cat = 170, table - cat = 130 => table is in the middle of those which is 150..
figured it out with both methods I'm pretty sure I won't be able to do it when I'm in grade school though
The funny thing is I dont think we actually know the height of the cat and turtle until we work out the height of the table, only the difference. I thought they were 40 and 20 and used those numbers at first.
I tried calculating those for an hour and failed miserably lol. Yes they are 40 and 20, but my primitive methods are clearly not enough to properly deduce them. Correction - different heights are possible
I got the height of the turtle visually immediately, then calculated the height of the table knowing the cat was 2 turtles height and the turtle was 20cm
The real height of the turtle and cat doesn’t matter at all. C=t+20, so you can pick any reasonable number with a 20cm difference and it doesn’t have to be 20cm and 40cm. I personally think for the sake of reality, 30cm and 10cm probably makes the most sense.
@@grassfedbutter Once you finish the table height you can go back and find out that the Cat is 30cm and the turtle is 10cm
@@davidbeck9066 You don't know the relationship between the cat and the turle (ignoring the picture given). The only thing you know is that the difference between their heights is 20 cm.
d = table
c = cat
t = turtle
two equations:
d+c-t=170
d+t-c=130
add both you get:
d+d+c+(-c)+t+(-t)=170+130
calculation result:
2d=300
divide by 2:
d=150
table is 150
I solved it with a third method. The difference in the two heights was 40 cm. The turtle was shorter than the cat so the difference in their heights was added to the table in one case (+ Cat - turtle) and subtracted from the other case (- cat + turtle) so you could add half the difference to the shorter or subtract it from the taller either gave 150cm
Luckily this question only ask the height of the table, not cat or turtle.
Otherwise, it would be unsolvable.
You have 3 unknowns but only 2 equations.
You won't solve the height of the other two
Cat is 40cm, turtle is 20
It can be anything as long as the difference(cat-turtle) is 20 cm
Cat=30, turtle=10 :)
Your Solution room is a line
My algebra was a bit more convoluted figuring that the cat was 20 cm larger than the turtle. Turns out it was a longer way of doing the same thing
How do you know how tall is the cat ?
Antonio Machado
We don't. But it isn't necessary to figure out.
Antonio Machado I figured the DIFFERENCE between their heights, not their heights.
I think you can also take the average of the two total high as well
I think this is the ONLY question I've been able to solve after watching dozens of videos on your channel.
i got distracted by a side mission when i am solving this question...
for the life of me i can't find the height of the turtle
can you help?