It is always great to see keen eyes and sharp mathematical minds at work. Thanks for sharing your observations below. 07:19, the 2 in the denominator in the formula is missing a power; it should be to the power of 8. 08:39, it can be noted that this inequality holds only for n > 3. If you spot additional errors, please continue to let us know in the comments. Remember, you have until the last day of June to submit your solution to us for Exercise 1 and 2. Solutions will be judged on their clarity of exposition and mathematical novelty. We will announce the winner soon after. Good luck!
I realize that the problem is mathematically based. However, there needs to be a visual / pattern recognition aspect to it also. Because there are patterns in the market and well worn paths, which are more familiar for price to go to (price history)
I think there are 2 minor errors in the video. At 6:35, n doesn't necessarily have to be even. Consider the case n = 3, it's still possible for the friends to meet. At 7:25, the constant in front of the sum should be 1/256, or 1/2^(2*4), instead of 1/2.
I wonder do optiver traders make such silly calculation mistakes when they're trading? It's honestly a worrying and not a great look on the company. Of course mistakes in the heat of the moment happen but when you're making a video like this that effort has been put in to script and animatination I don't know how mistakes are not caught. whoever animating 7:25 wrote out a probability much greater then 1 and no alarm bells went off?? good thing this mistake is on some harmless youtube video and not in some trade that is going to blow up the company's bankroll lol
@@leonmozambique533 you clearly have no clue what you are yapping about. Whilst the video may have errors - I suggest looking at the company's earnings - I think they are doing fine. (To note - if you worked in HFT you would know that the option markets around the world are pretty much dominated by these guys). Hot tip before you comment on youtube - get a clue
For ex2, I think there is something wrong with 1/n. For instance, when n = 2, P = 0.375 while 1/n = 0.5. P = 0.375 < 0.5 shows that P > 1/n is not true. I think it should be P > 1/(n+1). Please correct me if I'm wrong.
Because the formula is wrong. That is the formula for an n+1 by n+1 grid, not an n by n grid. When you plug in n=4, you get the answer for the original problem, which was a 5 by 5 grid. They need to substitute n with n-1 in the formula and then the answer becomes correct.
why no consider the cases that the steps take more than 4 steps, e.g first go to the top left, turn right, turn down, go to the bottom again, turn right and finally meet at bottom right
Thought the same. For n = 1, the two can meet at either (1,0) or (0,1). For n = 2, the two can at least meet at either (2,0) or (0,2). So, the two can at least meet at (n,0) or (0,n) for any positive integer n.
Some errors that I find in the video are:- 1. At 8:52 In Ex:2 it is not holding true for n = 2, for n = 2 the probability of meeting is 1/16*(1+4+1) = 3/8 < 1/2, so the proof should be asked for n>= 4. 2. Another Conceptual error that it is mentioned that probability of meeting for odd n is zero, this is not true actually that given formula is valid for all n,
It is always great to see keen eyes and sharp mathematical minds at work.
Thanks for sharing your observations below.
07:19, the 2 in the denominator in the formula is missing a power; it should be to the power of 8.
08:39, it can be noted that this inequality holds only for n > 3.
If you spot additional errors, please continue to let us know in the comments.
Remember, you have until the last day of June to submit your solution to us for Exercise 1 and 2. Solutions will be judged on their clarity of exposition and mathematical novelty. We will announce the winner soon after. Good luck!
More of this please, this is great!
I realize that the problem is mathematically based. However, there needs to be a visual / pattern recognition aspect to it also. Because there are patterns in the market and well worn paths, which are more familiar for price to go to (price history)
Depends if both are moving at the same speed... they could "binary tree" back to increase their probability.
I think there are 2 minor errors in the video.
At 6:35, n doesn't necessarily have to be even. Consider the case n = 3, it's still possible for the friends to meet.
At 7:25, the constant in front of the sum should be 1/256, or 1/2^(2*4), instead of 1/2.
I wonder do optiver traders make such silly calculation mistakes when they're trading? It's honestly a worrying and not a great look on the company. Of course mistakes in the heat of the moment happen but when you're making a video like this that effort has been put in to script and animatination I don't know how mistakes are not caught. whoever animating 7:25 wrote out a probability much greater then 1 and no alarm bells went off?? good thing this mistake is on some harmless youtube video and not in some trade that is going to blow up the company's bankroll lol
@@leonmozambique533 you clearly have no clue what you are yapping about. Whilst the video may have errors - I suggest looking at the company's earnings - I think they are doing fine. (To note - if you worked in HFT you would know that the option markets around the world are pretty much dominated by these guys). Hot tip before you comment on youtube - get a clue
7:46 The entire formula is wrong here because they say it's the formula for an n by n grid when it's actually the formula for an n+1 by n+1 grid.
7:32 There is a bug here! You forgot the power of 2, it should be (1/2) ^ 8
For ex2, I think there is something wrong with 1/n. For instance, when n = 2, P = 0.375 while 1/n = 0.5.
P = 0.375 < 0.5 shows that P > 1/n is not true. I think it should be P > 1/(n+1).
Please correct me if I'm wrong.
its for large n, your prob is 1/root(pi*n)
@@infinity624 Yes, that's also my answer for ex1 when n goes to infinity
Because the formula is wrong. That is the formula for an n+1 by n+1 grid, not an n by n grid. When you plug in n=4, you get the answer for the original problem, which was a 5 by 5 grid. They need to substitute n with n-1 in the formula and then the answer becomes correct.
Very educational! I hope you keep the series going!
I think there is something wrong with the explanation for the odd case, it shouldn’t be zero. Please check, it can still meet on the diagonals
Nice video, very well explained!
I'm not sure you are correct about the 'n must be even' thing. Doesn't really make sense, just try it with 2 and 4.
why no consider the cases that the steps take more than 4 steps, e.g first go to the top left, turn right, turn down, go to the bottom again, turn right and finally meet at bottom right
Very interesting challenge. I have just submitted my solutions :)
Where can I find more such sums to practice
Amazing!
When n = 5, if A only goes up and B only goes left, they should meet at the top left corner right?
exactly even for odd n that expression holds
Thought the same. For n = 1, the two can meet at either (1,0) or (0,1). For n = 2, the two can at least meet at either (2,0) or (0,2). So, the two can at least meet at (n,0) or (0,n) for any positive integer n.
@@cken27 For any positive integer n the two will always meet at one of the points (n-k, k) for 0
In the beginning it was said that this was to be constructed with a 4x4 grid; but the solution is portrayed with a 5x5?
Just in case, the edges of the map have 5 nodes to contain 4 spaces between the nodes.
Awesome 🙌🏻
Some errors that I find in the video are:-
1. At 8:52 In Ex:2 it is not holding true for n = 2, for n = 2 the probability of meeting is 1/16*(1+4+1) = 3/8 < 1/2, so the proof should be asked for n>= 4.
2. Another Conceptual error that it is mentioned that probability of meeting for odd n is zero, this is not true actually that given formula is valid for all n,
Probability is good but in market remove the problem by creating your direction
How is working in tradong and economics not enitrly BORING and DEPRESSING?