Per layer I count 4 singles+3 doubles+2 triples+1 MoaT so we've got 10 per layer. Any lower vertical layer can only be made a triangle by including the tip or it becomes trapeze. That in mind the same process repeats 4 layers in a row giving us 4*10 = 40.
I got 40, and the reasoning that that was all of them was sound and I knew it was sound. But I still spent a bit looking for the sneaky extra one(s) before I played the video.
If I knew this video existed, I wouldn't have created my own version of this animation. Except that I didn't upload it to RU-vid. You inspire me to create some silent videos. Thank you and well done :)
How did you come up with these values? It seems like you did a Gauss move times the number of squares on the lateral or on a row. But not sure how this logic works
@@imadoge5036 It is quite simple. Just take the uppermost 4 triangles. If you want to combine two of them to a larger one, there are three possibilities: the leftmost two, the two in the middle and the rightmost two. For a combination of three small triangles, there are two possibilities, and there is the large one consisting of all four small triangles. That is the 4 + 3 + 2 + 1 part. Now, do you know what homothecy is? If you combine one of the triangles in the upper row with the trapezoids of the lower rows, you get similar, bigger triangles. You can combine the triangles with the trapezoids of one, two, or all three rows below. That is the • 4 part.
Let’s see. There is 4 different triangle heights. There are 4 choices for containing no vertical internal lines, 3 for 1 vertical internal line, two for 2 vertical internal lines, and 1 for 3 vertical internal lines, so this is 4 * (4+3+2+1) or 40
Thank you for all your fabulous discussions about this video. I never expected it to get this much attention, and I love that it is entertaining so many people. 😘 Melissa
Exactly this. It's the wrong question. I was asked this at school and gave an answer and had a back and forth with the teacher that left him exasperated and about to draw on the board to show me, and I explained "I don't care how many triangles you say there ARE, I can only see (x) so the answer is (x)"
@@andypyne Math teachers are bad at explaining their problems. You can't take what they say to literally. For example 0*0=0. Well if I have zero of something zero number of times I would argue I always have something and never nothing. So the correct answer if you take the wording of 0*0= literally you should answer ="Anything but zero" not zero. 🤫
@@joakimsiljelind118 You're thinking 0/0 which is, mathematically, indeterminate (not to be confused by x/0, for non-zero x, which is undefined). But 0*0 is *always* = 0.
I came up with three answers: 0, 40, 41 If we look at this as a rectangle extending into the distance, it only looks like a triangle because of convergence in perspective. Thus, 0 actual triangles. If we do the common maths (4 + 3 + 2 + 1) x 4, as several commenters did, we get 40. Almost everyone forgets the triangle OUTSIDE. ((4 + 3 + 2 + 1) x 4) + 1 = 41
Original poster -- No, there is no "rectangle extending into the distance," so that answer is wrong. There is no "triangle on the outside," so that is wrong. There are only the triangles formed by the line segments. Your post is wrong. You can either amend it to correct it or delete it, else you are passing along false information.
@@robertveith6383 --- It's all a matter of perspective! This is one of the great things about math: things aren't always as they first seem. Sometime, find a nice long stretch of relatively straight road and actually observe. You will see a "triangle", even though your experience tells you the sides are parallel and not convergent. As for the triangle outside --- sometimes you need to derigidify your thinking.
THERE IS NO UNIQUE CORRECT ANSWER. For sure, there ARE 40 triangles. But the question is "How many triangles CAN YOU SEE?" If, for example, you can see only 4 triangles, and you say so, then you have answered the question correctly. Same for any other number of triangles that you can see. Maybe you can see 97 triangles. Right again! All joking aside, in math as in most every other endeavor, it is important to speak precisely and completely, so as to eliminate ambiguity and misunderstanding.
Counterargument: The question is "How many triangles CAN you see?" You might only recognize 4, or 5, etc., however, the fact is you CAN still see all 40. The definition of can is "to be able to," and there is no point in which you are incapable of seeing all 40 triangles, even if you recognize less.
@@julianmustermann1243"Can I have a sandwich" is wrong, "May I have a sandwich" is correct. "I can do it" means you have the ability to do it. "I will do it" means you will actually do it Every teacher will correct you when using "Can" the wrong way, but lots of people do use it the wrong way anyways... "Can" does not mean the same as "will" or "may" or "do," or anything else. Can is its own word for a good reason. It means something is possible, is able to happen...
It's only 5 because each line denotes the end of one object and the beginning of another so this video is wrong. Either you explicitly state 'you may combine multiple objects across dividing lines' or implicitly there are only 5, because there is 4 small triangles explicitly viewed, 1 grand triangle, and a bunch of quadrangle of various shapes. Combining a quadrangle and a triangle may make a larger triangle but without rules to explicitly express that it is not a condition you can infer. This is why our robots and AI fail so much, the lack of explicit instruction. You need to be clear what the rules are otherwise you get the right answer, just not the answer you thought it was.
So you ruled out all triangles with multiple parts, but decided to include the grand triangle with ALL parts I can see why our programs really fail now
Bro legit sounds like a robot and hey if you don't know the formula to find the number of triangles in such a figure then you don't have to justify your lack of skill, there is nothing to be ashamed of
Jesus mate. The utter stupidity with which you are basing your argument on is truly breathtaking. The “1 grand triangle” here is “made up” of what? 🤦🏾♀️ You are clearly not in robotics or any field that requires critical thinking. 🙄
We _can_ infer it, and we did. Claiming AI can only work with "explicit" (read: literal) instructions is to claim there is no real intelligence. It takes actual intelligence to look at a problem, see it several ways, and come up with a solution. Perhaps lack of ability to draw inference is not a failure to provide "explicit instructions" but is a failure of AI itself.
Your argument can directly, completely, and hilariously be turned right back against you. Sure, you weren't told that the shapes could combine to make more triangles, but, here's the kicker, _you weren't told they couldn't, either._
