Personally I see no value in converting to base 2 at the beginning. Step 1: 16^4(16-1) Then just calculate 256 * 256 * 15. It’s tedious but not too bad.
Agreed. Coming from computer tech its essentially 16 bit thus 65,536 then multiply it to 15. Its ending with 5 thus its not too hard of a multiplication.
Jajajaja..yo no estoy preocupado, pero si que su educación es una de las peores...no saben que inventar¡¡¡ es absurdo este problema, se lo está inventando...así les va¡
I'm not so sure why you'd use those 16^2 and 256^2, and not go straight to (2^16)*15 since I having studied programming a couple decades ago still do remember powers of 2 till 16th.
@@RammSkz Yes, I quite agree, I was just laying it out in simpler steps. I don't know where this fellow gets these little puzzles; frankly I'm doubtful that they are "entrance exams" for a place like Harvard, but if so, shame on Harvard because a question like this with all the power-of-2 emphasis is blatantly biased towards people with a pre-existing computer background!
For the final step, a neat trick I've learned for subtracting from a big number with several zeroes at the end is to subtract 1 from both numbers. That way you don't have to borrow a digit continuously. 1024000 - 40960 would become: 1023999 - 40959 You wouldn't have to borrow until you get to the 4 of the second number.
Simple factorisation yields 16^4x15. No serious University wants a prospective top undergraduate to do arithmetic. 256x256x15. What’s the point? Far more interesting question, given f(x)=x^n-x^(n-1), what does f(x) look like, n is even, n is odd, n>1 and is an integer. x is real.
f(x)=x^n-x^(n-1) --> f(x)=(x^(n-1))*(x-1) if you ever had to solve a problem like that, it's not hard at all. you have a formula for it x^a - x^b = x^a(1-x^b/x^a) or x^b(x^a/x^b-1) 16^4 * 15 is the same as 16^5 * 15/16
You don't need the first part with basing it of two. You can directly change it to 16^4*15 and from there I would just go brute force. 16^2=256 anyone should know this if he taking this test, so it is basically just 256*256. Most people probably know 2^n for n up to 16 or something this would basically solve it instantly and *15 is of course really easy.
That is the dumbest math operation I have ever seen!!!! It is simply 16 to the power 4 common times (16-1) which is simply 16 to the power 4 times 15 and that is 983040.
16^5-16^4 = 2^20-2^16 = 2^10*2^10-2^16 = 1024*1024-65536 = 983040 Just one simple multiplication and a substraction. If you can't do this by hand, go back to school.
My way: Factor out: 16^4 * 15 Recognize: 16^4 = 65536 Calculate: 65536 * (10 + 5) = 655360 + 327680 = 983040 It helps to know the powers of two; need them for bitflags when programming anyway. Also times 5 is just half and add a zero :)
When I went to mit and I applied to Harvard and all the ivy schools in late 70s zero had an entrance exam. They looked at my act (that’s what I took in high school) now the sat is used and I had to write an essay on application and do an interview. No Ivy League or mit has an entrance exam. There are tests to place you after acceptance but optional like every university. Some kids totally bypassed calculus because they aced it (not me) but they get 10s of thousands of applications and it would be a nightmare to give entrance exams to all of them. It’s a ridiculous idea. And then to put some 9th grade algebra problem on it is even dumber. Maybe this is for some bogus Harvard mail order university. Not the real one.
16^5- 16^4 , supongamos que a = 16 entonces la ecuacion quedaria a^5-a^4 = a^4*a - a^4 y si b = a^4 entonces quedaria b*(a -1) = y sustituyendo el valor de a = 16 entonces seria b*(16-1) = b*15 = 15b multiplicariamos entonces los valores con el resultado 15b = 15 * a^4 = 15 * 16 * 16 * 16 * 16 = 983040 .. Mas simple... Obvio con la cacluldadora solo basta presionar los botones ... jejejeje
Con los mismos Valores seria 16^5-16^4 = 16^4*16 - 16^4 = 16^4(16-1) = 16^4*15, lo bonito de la matematicas es el que aprendes a utilizar logica que aplicaras toda la vida para resolver problemas de la vida real, somos seres analiticos
This is not an equation, but an expression. Then the follower arrow and the equal sign are confused. Brackets are different sizes. There are no squares on the paper.
The number of steps is unnecessary 16^5 - 16^4 = (16 - 1 ) * 16^4 = 15 x 16^4 = (15 * 16 * 16 * 16) * 16 | from here on it is simple addition and multiplication = 240 * 256 * 16 | problem of large number multiplication - but easy if you know the power of two = (51200 + 10240) * 16 | from here it is only grunt work only showing the elimination of one operator at a time. = 61440 * 16 = 61440 * ( 15 + 1 ) = 614400 + 307200 + 61440 = 614400 + 368640 = 983040
I've interviewed with Harvard, they don't give you a math test. You interview with alumni based in your area who participate in their interview process. there are no test
A computer can solve this problem in a nanosecond....humans (including those who matriculate at Harvard) have painfully slow processing skills. This video is prima facie evidence that this is so.
@@ddal3998 Indeed, BUT computers have mathematically superior intelligence than us mere humans. The future of mathematics will fabulously favor the computer to the drudgingly slow mental processes of our species...no matter how gifted or developed the individual's mind.
I initially tried to do this with 2^5 - 2^4 and got the answer 2^4. So I thought the answer would be 16^4. Turns out it isn't the same for base 16 as it is for base 2, lol. Still, it's kinda funny that 2^5 - 2^4 = 2^4.
So one of the Earth’s top 10 Universities ask that level 3 question as an entrance test …..?……..to study a degree requiring an excellent knowledge of Maths ? Surly this cannot be the case ?
Not really. If you are doing mental math, these are the steps you go through. He just wrote it down. People tend to work with round numbers more easily. So he was just converting everything to round numbers until the end. However, this approach only makes sense if you don't have a calculator. If you do, then this entire exercise is irrelevant.
Personally I see no value in converting to base 2 at the beginning.
Step 1: 16^4(16-1)
Then just calculate 256 * 256 * 15. It’s tedious but not too bad.
Thank you, my thoughts also. I was watching this and thought what the hell is he doing.
Yes
Agreed. Coming from computer tech its essentially 16 bit thus 65,536 then multiply it to 15. Its ending with 5 thus its not too hard of a multiplication.
Not even all that tedious, to those of us old enough to have been drilled extensively in long multiplication at the age of seven.
Exactly what I did. No point in the extra factoring.
if this is Harvard entrance exam, I am seriously worried about US education system.
No
For real
🤣🤣🤣🤣Indeed it is toooooooooooooooooooooooooooooooooooooo simple 16⁵-16⁴=15*16⁴
Don't worry they get all Nobel prizes...
Jajajaja..yo no estoy preocupado, pero si que su educación es una de las peores...no saben que inventar¡¡¡ es absurdo este problema, se lo está inventando...así les va¡
This took longer than just multiplying 16 by 16 a bunch of times
Do it in hexadecimal. 0x100000 - 0x10000 = 0xf0000. There's your answer.
And now to convert it to decimal, simply calculate 15*65536.
@JackRussell021 now that's genius in simplicity
Coming from a computer engineering background, simpler to me to view as 16^2 = 256 and 256^2 = 65536, so 65536 * 16 - 65536, or 65536 * 15.
...and also being familiar that 65536 / 2 = 32768, to calculate on paper I'd go with 655360 + 327680.
I'm not so sure why you'd use those 16^2 and 256^2, and not go straight to (2^16)*15 since I having studied programming a couple decades ago still do remember powers of 2 till 16th.
@@RammSkz Yes, I quite agree, I was just laying it out in simpler steps. I don't know where this fellow gets these little puzzles; frankly I'm doubtful that they are "entrance exams" for a place like Harvard, but if so, shame on Harvard because a question like this with all the power-of-2 emphasis is blatantly biased towards people with a pre-existing computer background!
0b1111 0000 0000 0000 0000
@@RammSkz
This is what i had in mind that should be the answer at first
I'm surprised that he really did the calculation
A long way to solve a simple equation!
And it's not even an equation to be solved. It's just an expression to be calculated.
What's the easy way????
If you from Harvard you don’t look for simple solutions you need to show everyone why you have the diploma
@@chartedtravel1776 That's why the USA is crap at inventing things. Oxford.
@@lk6789factor out 16 to the fourth power. This leaves 16-1=15. 16 to the fourth power times 15=983040. Easy peasy!
For the final step, a neat trick I've learned for subtracting from a big number with several zeroes at the end is to subtract 1 from both numbers. That way you don't have to borrow a digit continuously.
1024000 - 40960 would become:
1023999 - 40959
You wouldn't have to borrow until you get to the 4 of the second number.
Simple factorisation yields 16^4x15. No serious University wants a prospective top undergraduate to do arithmetic. 256x256x15. What’s the point?
Far more interesting question, given f(x)=x^n-x^(n-1), what does f(x) look like, n is even, n is odd, n>1 and is an integer. x is real.
f(x)=x^n-x^(n-1) --> f(x)=(x^(n-1))*(x-1) if you ever had to solve a problem like that, it's not hard at all. you have a formula for it x^a - x^b = x^a(1-x^b/x^a) or x^b(x^a/x^b-1)
16^4 * 15 is the same as 16^5 * 15/16
2^20-2^16 = (2^10)^2 - (2^8)^2 = (2^10+2^8)(2^10-2^8) by difference of squared formula = (1024+256)(1024-256)=1280x768=983040
You don't need the first part with basing it of two. You can directly change it to 16^4*15 and from there I would just go brute force. 16^2=256 anyone should know this if he taking this test, so it is basically just 256*256.
Most people probably know 2^n for n up to 16 or something this would basically solve it instantly and *15 is of course really easy.
Every programmer knows 2^16 = 65,536. We've all accidentally blown up an integer counter at some point...
1) 16
2) 16 x 16 = *256*
3) 16 x 256 = *4.096*
4) 16 x 4.096 = *65.536*
5) 16 x 65.536 = *1.048.576*
1.048.576 - 65.536 = *983.040*
Yep
16^5 −16^4 =16^4 ⋅(16−1)=16^4 ⋅15
; 16^4 = 65536
and 65536⋅15=983040
Harvard does not have an “entrance” exam. Like every other university in USA it uses standardized SAT exams to evaluate applicants.
That is the dumbest math operation I have ever seen!!!! It is simply 16 to the power 4 common times (16-1) which is simply 16 to the power 4 times 15 and that is 983040.
Ridiculous. It is as simple as 16^4*1*. Why all those extra calculations?
16^5-16^4=16^4(16-1)=15*16^4 .............. calculated in 5 seconds
I'll just use a calculator
16^5-16^4 =
2^20-2^16 =
2^10*2^10-2^16 =
1024*1024-65536 =
983040
Just one simple multiplication and a substraction. If you can't do this by hand, go back to school.
If they didn't specify a base for the answer, it's just F0000 in hexadecimal.
My way:
Factor out: 16^4 * 15
Recognize: 16^4 = 65536
Calculate: 65536 * (10 + 5) = 655360 + 327680 = 983040
It helps to know the powers of two; need them for bitflags when programming anyway.
Also times 5 is just half and add a zero :)
16^4×16-16^4=16^4×15=2^16×15=65536×15=655360+327680=983040
20 seconds if you know 2^16=65536
16^5 = (16^4)*16 ….. therefore …. 16^5 -16^4 = 16^4*(16-1) =(16^4)*15….
or more generally, (n^x+1) - (n^x) = n-1(n^x)
16^4 (16-1) = 256x256 x15
16^5 - 16^4 = x
16(16^4) - 16^4 = x
16(16^4) - 16^4 / 16^4 = x/16^4
16-1 = x/16^4
15 = x/16^4
15(16^4) = x
Guy never fails to amuse me.
When I went to mit and I applied to Harvard and all the ivy schools in late 70s zero had an entrance exam. They looked at my act (that’s what I took in high school) now the sat is used and I had to write an essay on application and do an interview.
No Ivy League or mit has an entrance exam. There are tests to place you after acceptance but optional like every university. Some kids totally bypassed calculus because they aced it (not me) but they get 10s of thousands of applications and it would be a nightmare to give entrance exams to all of them. It’s a ridiculous idea. And then to put some 9th grade algebra problem on it is even dumber. Maybe this is for some bogus Harvard mail order university. Not the real one.
16^5 - 16^4
= 16^4 (16 - 1)
= (2^4)^4 * 15
= 2^16 * 15
= 2^10 * 2^5 * 2 * 15
= 1024 * 32 * 30
= 1024 * 960
= (1000 + 24) * (100 - 4) * 10
= (100000 - 4000 + 2400 - 96) * 10
= (100000 - (4096 - 2400)) * 10
= (100,000 - 1,696) * 10
= (98,304) * 10
= 983040
16^5- 16^4 , supongamos que a = 16 entonces la ecuacion quedaria a^5-a^4 = a^4*a - a^4 y si b = a^4 entonces quedaria b*(a -1) = y sustituyendo el valor de a = 16 entonces seria b*(16-1) = b*15 = 15b multiplicariamos entonces los valores con el resultado 15b = 15 * a^4 = 15 * 16 * 16 * 16 * 16 = 983040 .. Mas simple... Obvio con la cacluldadora solo basta presionar los botones ... jejejeje
Con los mismos Valores seria 16^5-16^4 = 16^4*16 - 16^4 = 16^4(16-1) = 16^4*15, lo bonito de la matematicas es el que aprendes a utilizar logica que aplicaras toda la vida para resolver problemas de la vida real, somos seres analiticos
You choose the long road, what if I told you that the solution is in two lines?
16^5 = 16 * 16^4.
16*16^4 - 1*16^4 = 15* 16^4
16^4 = 65536
15 * 65536 = 983040.
This is not an equation, but an expression. Then the follower arrow and the equal sign are confused. Brackets are different sizes. There are no squares on the paper.
Unnecessary complications 😂
16-1=x/16^4 => 15(16^4)=x => 983040=x there I made it easy
Nice write up
Btw, I don’t think I’ve ever seen number 4 and 9 being written the way you do it
16⁵ - 16⁴ = 16⁴×( 16-1) = 16⁴ × 15 ✓
The number of steps is unnecessary
16^5 - 16^4
= (16 - 1 ) * 16^4 = 15 x 16^4
= (15 * 16 * 16 * 16) * 16 | from here on it is simple addition and multiplication
= 240 * 256 * 16 | problem of large number multiplication - but easy if you know the power of two
= (51200 + 10240) * 16 | from here it is only grunt work only showing the elimination of one operator at a time.
= 61440 * 16 = 61440 * ( 15 + 1 )
= 614400 + 307200 + 61440
= 614400 + 368640
= 983040
In other words, Harvard’s law is “Why do it simple when it can be made complex"
It's quicker to calculate (16-1)*16p4 as 16p5=16*16p4
We don’t need children to be fast in math, calculators are fast, we need children to be thinkers - Dr Yeap Ban Har
Take 16^ 4 as common then we get 16^4×15
2^4×8^4×15
16×15×8^4
240×8^4
240×2^12
24×10×(2^6)2
24×10×64×64
983040
I've interviewed with Harvard, they don't give you a math test. You interview with alumni based in your area who participate in their interview process. there are no test
what an insult to the many great mathematicians in Italian history
more reasonable to stop at 960 *1024 and simply say
960 K_Bytes.
Computer scientist here: it's 1 megabyte - 65536
It's not that hard.
16^5-16^4=
(16-1)*(16^4) =
15*2^16=
15*2^6*2^10=
15*64*2^10~1000*1000=
1.000.000 give or take 5%
16*4 common lelo 4 stap me answer Aa jayega
carefully explains his work calculating 64x5 and then just casually writes the answer to 1024x40
16^5 -- 16^4 = 16^4(16 -- 1) = 15*16^4 = 15* 16^2 * 16^ 2 = 15*256*256 = 983,040
15(16^4)
= 15(2^16)
= 15(1024)(64)
= 15360(60+4)
= 921600+61440
= 983040
Con los mismos Valores seria 16^5-16^4 = 16^4*16 - 16^4 = 16^4(16-1) = 16^4*15
A computer can solve this problem in a nanosecond....humans (including those who matriculate at Harvard) have painfully slow processing skills. This video is prima facie evidence that this is so.
It's not about who solves faster, it's about developing mathematical mind.
@@ddal3998hmmm, i feel like some students at harward and other colleges care more about antisemitic hysteria than study.....
@@ddal3998 Indeed, BUT computers have mathematically superior intelligence than us mere humans. The future of mathematics will fabulously favor the computer to the drudgingly slow mental processes of our species...no matter how gifted or developed the individual's mind.
@@jamesreed1969 🤭
While at Hogwarts University you just need a magic wand and the spell "Solutio Equatio"😉
I did this in my head in under 1 minute.
That's cheating, you saved the time for writing 😅
I guess it's simpler to just multiply 16, 5 times, then substract the 16⁴ since its already counted. 😂
Solve the equetion please 1/(x-1)^2+1/(x-2)^2=1/x^2
Straight forward post 16 algebra question. Nowhere near undergraduate level. You’d expect the solver to state undefined for x=0, 1, 2 as well.
16'4*15=256*256*15=15(51200+12800+1536) =65536*15=655360+327680=983040
Much ado about nothing
I initially tried to do this with 2^5 - 2^4 and got the answer 2^4. So I thought the answer would be 16^4. Turns out it isn't the same for base 16 as it is for base 2, lol. Still, it's kinda funny that 2^5 - 2^4 = 2^4.
And I just realized why as well. If you do the same factoring as 16^4(16-1), you get 2^4(2-1), which as you can see is just 2^4(1), lol.
When you realize it's not 16, it's easy.
А мы это в школе в 9 классе делаем...
16*16*16*16*15=256*256*15, 3 till 5 th year elementary school class. Harvard ?
What?? x=16^4, so x(16-1), so 15*16^4
16^5-16^4=16^4*(16-1)=16^4*15=2*2^10*2^5*3*5=2*5*3*2^10*2^5=10*3*1024*32=30*32*1024=960*(1000+24)=960000+960*20+960*4=960000+19200+3840=960000+23040=983040...
15 y/o should be able to solve it. As a Harvard question, it is simple.
=16^4×15. ////
Nice
Thanks
This is about the most complicated way to solve this!
This was...interesting. But are you sure you didn't use too many steps?
Why didn't you simply convert everything to single numbers at the beginning? University should be capitalized!
And solution is primary class level of india
16^5 - 16^4 = 16 * 16^4 - 16^4 = 15 * 16^4
I can solve this in 30 seconds on my phone calculator..lol
3:08 He realises that 64*5 is just half of 64*10 in 3... 2... 1...
I just use Matlab…
ça fait 16⁴(16-1) =15x16⁴ = 15x2¹⁶ = 65536x15 = 983040
Much too long to calculate. Try factoring: 16**5 - 16**4 = 16**4(16 - 1) =16**4 * 15 = 983,040.
What language is this vid in?
Well, if you're absolutely set on doing it the complicated way ...
When in my exam paper they mentioned write solution in 10-15 steps i will do this 😂😂😂
Warum so kompliziert?!?
16'5-16'4=16'4(16-1) =16'4*15
It's too easy to be solved what you called it Harvard University equation
Uuh, Harvard Elementary School.
16^5-16^4=16*16^4-1*16^4=15*16^4. Who cares what the actual number is.
That is NOT an equation. It is an expression, there is nothing to solve.
youtube should active an IQ donation option for channels like these.
So one of the Earth’s top 10 Universities ask that level 3 question as an entrance test …..?……..to study a degree requiring an excellent knowledge of Maths ?
Surly this cannot be the case ?
too complicated 😢
Not really. If you are doing mental math, these are the steps you go through. He just wrote it down. People tend to work with round numbers more easily. So he was just converting everything to round numbers until the end. However, this approach only makes sense if you don't have a calculator. If you do, then this entire exercise is irrelevant.
😂😂😂😂😂
(15/16) x 16^4.
I am shocked by seeing this kind of questions !
Me, 16x16 five times minus the 16x16 four times
Harvard? I have my doubts.
its trending tag😊
🤘
(16*16*16*16*16)-(16*16*16*16)
Why so complicated ? should be 15 x 256^2.
this guy would not have made it imtui Harvard, he couldn't do 16^4 * 15? really?
Why are unnecessarily increasing no. of steps😂