Thank you sir . I am from Sri Lanka I had difficulty to understand how to solve questions based on solving trigonometry identities . Now I understood by how to solve them . Thank you so much sir ☺️
Man, I have another challenge for you. And by "challenge" I mean a problem that I'm too stupid to solve on my own. So, you know that grid pattern that you have to draw on a smartphone lock screen with your finger to unlock it? Like, 9-dot grid line. I was wondering how many possible combinations I can make out of it. At first, I substituted dots with numbers from one to 9, making it look like a permutation problem. So basically the answer could be 9!, but alas, I can't go from 9 to 3 without touching 6. So I just counted the number of combinations that are not satisfying that condition, getting the number 16. So my answer is 9! - 16, but I'm not quite sure that I really considered all the cases. Can you help me out?
@@mathonify 9, at least in the case of my problem. It is 3*3 grid made of dots from the smartphone lock screen. Like that: www.google.com/search?q=smartphone+pattern+grid&rlz=1C1CHBD_ruUA869UA869&sxsrf=ALeKk01wQwlzekkSutohudvhU1Kadmd9pg:1606233611376&source=lnms&tbm=isch&sa=X&ved=2ahUKEwi2ydO-xpvtAhW2BhAIHQ8WAscQ_AUoAXoECAUQAw&biw=1440&bih=753#imgrc=bYvSZilWW4nMMM
Ok and how many “numbers” in the unlock code? I mean is there a limit to how many dots can be in the “unlock pattern” or could you create an unlocking pattern with more than 4 dots to connect? In other words when you unlock your phone, how many dots are in the pattern to unlock the phone?
@@mathonify ahah ^.^ I'm really sorry for my English proficiency :3 On my phone, there are 9 "numbers", from 1 to 10, three in each line and row. So I want to solve the problem when I have 9 dots ( 3×3 ) to connect, but in general, there is no limit of course. You can imagine a grid with an unlimited number of dots. But there is no way I will come up with a general formula
I understand that the grid has 9 dots, but how many need to be in the unlocking pattern? Like when you go to unlock the phone, what pattern will you make to unlock the phone? how many dots in that pattern? e.g the example you linked had a code of 1-4-7-8 which is a 4 digit code. So is the number of digits in the unlock code limited to 4?
Thank you sir . I am from Sri Lanka
I had difficulty to understand how to solve questions based on solving trigonometry identities . Now I understood by how to solve them . Thank you so much sir ☺️
Nicely presented.
Great refresher. Thank you 😊
I was really in need of them TY❤
Awesome playlist, thanks!
So basically I have to solve like 10000 questions just to grasp the ability to figure out what to do for each case
Although before this video I would have needed 1 million questions
Man, I have another challenge for you. And by "challenge" I mean a problem that I'm too stupid to solve on my own.
So, you know that grid pattern that you have to draw on a smartphone lock screen with your finger to unlock it? Like, 9-dot grid line.
I was wondering how many possible combinations I can make out of it. At first, I substituted dots with numbers from one to 9, making it look like a permutation problem. So basically the answer could be 9!, but alas, I can't go from 9 to 3 without touching 6. So I just counted the number of combinations that are not satisfying that condition, getting the number 16. So my answer is 9! - 16, but I'm not quite sure that I really considered all the cases. Can you help me out?
How many dots need to be in the code? Is it 4?
@@mathonify 9, at least in the case of my problem.
It is 3*3 grid made of dots from the smartphone lock screen.
Like that: www.google.com/search?q=smartphone+pattern+grid&rlz=1C1CHBD_ruUA869UA869&sxsrf=ALeKk01wQwlzekkSutohudvhU1Kadmd9pg:1606233611376&source=lnms&tbm=isch&sa=X&ved=2ahUKEwi2ydO-xpvtAhW2BhAIHQ8WAscQ_AUoAXoECAUQAw&biw=1440&bih=753#imgrc=bYvSZilWW4nMMM
Ok and how many “numbers” in the unlock code? I mean is there a limit to how many dots can be in the “unlock pattern” or could you create an unlocking pattern with more than 4 dots to connect? In other words when you unlock your phone, how many dots are in the pattern to unlock the phone?
@@mathonify ahah ^.^
I'm really sorry for my English proficiency :3
On my phone, there are 9 "numbers", from 1 to 10, three in each line and row.
So I want to solve the problem when I have 9 dots ( 3×3 ) to connect, but in general, there is no limit of course.
You can imagine a grid with an unlimited number of dots.
But there is no way I will come up with a general formula
I understand that the grid has 9 dots, but how many need to be in the unlocking pattern? Like when you go to unlock the phone, what pattern will you make to unlock the phone? how many dots in that pattern? e.g the example you linked had a code of 1-4-7-8 which is a 4 digit code. So is the number of digits in the unlock code limited to 4?