Chinese College Entrance Exam Math question. How many of you will be qualified to get into a Chinese university?

>>16715634 (OP)
This is why china has room temperature superconductors, working fusion power generation technology and hyper efficient and advanced AI that is close to achieving true AGI status.

>>16715634 (OP)
>western universities having entrance exams
That would reduce the number of teenagers you can endebt to you. It’s also illegal in places like the UK where successive governments have mandated 50% of the population no matter of ability is sent into uni, all to give the illusion of progress.

Unis aren’t about education. If they were there’d be strong selection systems to get in, half my course dropped out by the end of it.

>>16715634 (OP)
1) (1,2), (1,6), (5,6).
2) Suffices to prove the case when m=3, in which case it is clear, as (a_1,a_4,a_7,a_10), (a_3,a_6,a_9,a_12), and (a_5,a_8,a_11,a_14) are arithmetic sequences.
3) Have seen P_1>1/8. If (a_1,\dots,a_{4m+2}) is (i,j)-separable, then (a_1,\dots,a_{4m+6}) is (i,j)-separable. Moreover, this sequence is (n,4m+6) whenever n=1(mod 4), and is (n,4m+5)-separable whenever n=2(mod 4) and n<4m+2. Additionally, the sequence is (1,4m+6)-separable and (4m+5,4m+6)-separable. Hence, there are at least an additional 2m+2 pairs (i,j) making the sequence (a_1,\dots,a_{4m+6}) (i,j)-separable compared to the sequence (a_1,\dots,a_{4m+2}). Since there are an additional 4(4m+2)+6=16m+12 total pairs (i,j), and (2m+2)/(16m+8)<1/8, then P_{m+1}<max(P_m,1/8)<1/8, by induction.

>>16715658
Sorry, should be (2m+2)/(16m+8)>1/8, so P_{m+1}>min(P_m,1/8)>1/8.

>>16715658
But (2) says m greater than or equal to 3, not just equal.
I got the same answer for m = 3, but the goal is to generalise it for m = 4, 5, 99, so on.
So, we add another 4 terms to a, to form one extra subsequence, none of which must contain element 2 nor 13, yet must be evenly spaced, by m distance.
Hence, the numbers (n) can be separated modulo m: n mod m, n+1 mod m, ... m-1 mod m, and each 4-length subsequence will be entirely contained within one of these divisions.
If 2 or 13 are in one of these divisions, they are skipped. To prove this, for m >= 3: 2 and 13 must be the first or (modolu 4) first element, so a gap can be left without sequences breaking an arithmetic sequence. 2 is a prime number, and as 2 < 3, must always be the first, so QED. 13 is also a prime, and 13 = 4*3+1 = 1 (modulo 4) so also QED.

So, m = 3, the arithmetic sequence a1 to a(4m+2) is 2,13-separable.
And, if m - 1 is a 2,13 separable sequence, then so is m,
Therefore, all sequences m >= 3 are (2,13)-separable.

>>16715690
Dickhead, you don't need to write all that down to recognize that (a_{4m+3}, a_{4m+4}, a_{4m+5}, a_{4m+6}) is arithmetic.

>>16715693
sorry my proofs are always verbose as fuck
i never did the practice questions / paid attention enough so i just hit it with intuition until it works

>>16715634 (OP)

Chinese College Entlance Exam Math question:

1) Why is Chinaman histoly wlitten in London?
2) Why are Chinamen banklolled by Washington?
3) Why don't Chinamen have dietaly laws, something that distinguishes humans flom animals?

Now post isi and cmi's math entrance qp for their Bsc and Msc programmes OP

>>16715696
Anon, your intuition is severely deficient.

>>16715634 (OP)
Is This supposed to be a hard question from the test?
In my country, which is a "turd" world country, depending on which college you want, the test questions are much harder than this.

Don't understand shit
I can only handle concrete numbers.

t.brainlet

>>16715634 (OP)
a) 1 2 , 5 6
b) because you can separate the indices according to their value mod m, and the sequences you get are arithmetic progressions of size 4
c) I dunno you probsbly multiply a lot of shit together like it’s independent events. or ninduction if your gay

>>16716357
>American education

>>16715642
Implessive

>>16716387

>>16715634 (OP)
This isn't a college entrance exam in China because I knew freshmen Chinese students in prestigious universities who couldn't understand simpler stuff and they went to study abroad because their unis weren't as good (at least at the time). You definitely see pre-university people dealing with stuff like this but it's usually IB HL or extended math students on a fast track to Oxford. Speaking from personal experience.
(1) and (2) are easy but mixed topic questions like (3) are too advanced for regular college entrance exams. In many countries regular HS curriculum doesn't cover probability.

>>16715634 (OP)
>Chinese Collee Entrance Exam
>500 questions you must complete in one hour which the proctor then bins because your father isn't a Party member or your aunt has a low social credit score.

>>16718965
>>500 questions you must complete in one hour which the proctor then bins because your father isn't a Party member or your aunt has a low social credit score.
that is a good thing, you capitalist pig

>>16715642
>This is why China has BUZZWORD, BUZZWORD and BUZZWORD!!!!
>China numba one!!!!
>Erm.. chuddy, wanting to see the technology is heckin raycist!!!

>>16715634 (OP)
aren't you fuckers bored with this kind of shit already? chinese college entrance exam problem, indian college entrance problem, homo floresiensis college entrance problem, you should be able to solve this etc.

(((Universities))) are centers for Satanic indoctrination.