A Combination Equation (n choose r = 1984)

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[mdperpe]

@14:00. It should be 1984 = 2^6 * 31, not 2^4 * 31.

[bprpfast]

I have never even thought about this kind of equations. Just wow!!!

[davidgillies]

But 1984 = 2^6 . 31. Fortunately it doesn't affect the result.

[moonlightcocktail]

2^2, 2*2, 2+2th
1984 = 2*2*2*2*2*2*31...
(nCr) has a prime p as a factor => n>p
Proof: Suppose not. Then n<p and nCr = n(n-1).../r! But no p appears in the denominator of nCr. Contradiction.
...?
Also, r>3 and we only consider r up to n/2
Unproven: For all n, r s.t n>31, r>3, and r<n/2, (nCr) > 31C3. (Left as an exercise to...)
Since 31C3 = 4495, no other solutions exist.

[math]

you expand my knowledge everytime I watch, great job

[richardryan]

At about 5:10 you stated that, if r >= 3, then C(n, r) >= C(n, 3), which is not always true. For example, if n >= 4, then C(n, n) = 1 < C(n, 3). It appears that an upper bound for r needs to be specified. As Per Persson suggests, r <= n - 3 is one possibility choice when n >= 6.

[PunmasterSTP]

Wow, I'm not sure if I've ever come across a problem like this before! I feel like I'm constantly learning new things when I watch your channel, and I'd like to say thank you and keep up the outstanding work!

[DianeCastle]

If n = 2^4 * 31, then you can write it as 32*31/2 which is (32 2). You meant n = 2^6 * 31.

[carloshuertas]

Wow, another great explanation, SyberMath! This is the first time I see this formula.

[鈴木悠真-nz]

I love how you end this video.
Be safe. Take care.
And bye bye.

[rafael]

I have had to watch the video two times to understand some things, but great!! Very well explication!!

[leecherlarry]

i tried various approaches but my computer couldn't spit out these 2 trivial solutions lol

[mdperpe]

"If r≥3" should be "If r≥3 and r≤n-3".

[cfgauss]

If it were a do or die situation, I would have just drawn Pascal's Triangle to see if 1984 appears anywhere else besides the whole number diagonal. But very nice explanation (although did you really need the calculus?)

[markobavdek]

Cool!
I forgot this stuff a little bit. This is quite a recall.

[ramaprasadghosh]

1984 = 992 *2 = 496*4 = 248 *8
= 124 *16= 62*32=31*64
n choose r being equal to 31 *64,
the prime number 31 must be a factor of n choose r..
Hereby n must be 31 or more.
Now
31 choose 2 = 15*31 < 31*64
31 choose 3 = 5*31*29 > 1984
Now 32 choose 2 = 16*31 < 31*64
32 choose 3 = 16*31*15 > 1984
and 33 choose 3 = 11* 16*31 > 1984
Hereby no feasible solution is there for any r of value 2 or more .

Thereby only solution to n choose r is for r =1, n = 1984.

[ekut]

alternate title, solving George Orwell's 1984 mathematically

[khaledqaraman]

Well... The inequality at 5:10 is wrong !!
For example : Note that 10 C 10 = 1 < 10 C 3

[Mathcambo]

The teacher is really good. I will learn from. I will make a video following the teacher to share with everyone.

[muskamelogbi]

Dear professor may l ask you a question is optimization calculus an exception or a part of infinitésimal calculus ? Thanks lot