M
medicine is a part of science
So are geography and sociology, they are social sciences.
But the S in STEM doesn't refer to all sciences
Over
If an oven can bake one cake every hour,
how many cakes can 40 ovens bake in 3 years?
A
Is that a Holocaust reference or am I way too far gone?
If you forget the cake in the oven for too long it will surely become holocausted down to ash.
C
why is this still pinned?
Because it's the HIGHEST IQ thread on the site
Duh
Tldr
Finally, some good fucken high IQ level thread, get them one of the Guidorizzi's books so they can whack their brains in OP
Just remembered this one is brazilian, might be hard to understand the question, maybe a Strang or Stewart might be better
When your realize that your qt foid STEM class coleague chooses to be declared volcel but in reality fucks a chad a day just like everyone else but you you might end up in here too
Consider the function f(n), such that f(0) = 0 and f(⌊n/10⌋) + n - 10⌊n/10⌋, how many algorisms does the smallest positive integer m has, such that f(m) = 2015?
Is the function f(n) defined by f(n) = f(⌊n/10⌋) + n - 10⌊n/10⌋? You didn't make that clear
def f(n):
if n == 0:
return 0
else:
return f(n // 10) + n - 10 * (n // 10)
m = 1
power = 10
algarism_counter = 1
while True:
if f(m) == 2015:
break
m += 1
if m == power:
power *= 10
algarism_counter += 1
print("m has:", algarism_counter)
Could only count to 9, gave up
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What is that? Why do you write like a computer?
It's code in python for calculating functions with recursive method, but it took so much heap for a long time that I could only see m reaching 9 algarisms, by the way what is the actual answer I'm curious
It's higher than 200 bhai.
Also, why do you use that? YOU CAN'T USE PYTHON AT OLYMPIAD
I don't think it's anywhere near 9. The highest possible value for n - 10(⌊n/10⌋) is 9, so there's at least 223 algorithms. Idk how you can do this question without brute force, which is already impossible.
Didn't know that, sorrie. Also, I reckon floor functions are not differentiable, so I assume you can't use derivatives on this one for m to reach 2015, how do you solve it?
It's from a high school olympiad, you can solve it without calculus.
I haven't solved it
Ye, no heap anywhere near as capable of reaching this result
Apes should live comfortable life in the jungle, not this shit!!!!
Let V be a vector space with dim(V) = n < ∞. Suppose that L: V -> V is a linear map and that 0 is an eigenvalue of L.
Prove that L cannot be surjective.
Prove that L cannot be surjective.
If 0 is an eigenvalue, then there exists a non-zero vector in the kernel, which means it's nontrivial so dim(L(V)) < n. Therefore, L is not subjective.
hey good job. i know it wasnt the most challenging problem, but i just wanted to throw in a cute little algebra problem
A
I think Chad can always force a win. First, Chad takes away 2 stacks. After that, he keeps mirroring Pepe's move. I didn't check super thoroughly, but I think this works.
A
I'll just find the smallest m s.t. f(m) = 2015. Given that the algorithm is already specified, I don't really understand the "how many algorithms" part of the question.
For n < 10, f(n) = n
For 9 < n < 100, f(n) = ⌊n/10⌋ + n - 10⌊n/10⌋ = n - 9⌊n/10⌋
For 99 < n < 1000, f(n) = ⌊n/10⌋ - 9⌊⌊n/10⌋/10⌋ + n - 10⌊n/10⌋ = n - 9⌊n/10⌋ - 9⌊n/100⌋
For 999 < n < 10,000, f(n) = ⌊n/10⌋ - 9⌊⌊n/10⌋/10⌋ - 9⌊⌊n/10⌋/100⌋ + n - 10⌊n/10⌋ = n - 9⌊n/10⌋ - 9⌊n/100⌋ - 9⌊n/1000⌋
The pattern should be clear by now. If n has digits abcd with a > 0, then f(n) = abcd - 9(abc + ab + a) = a + b + c + d. At this stage, it should be easy to convince yourself that f is just the digit sum function.
The smallest number with digit sum 2015 is an 8 followed by 223 9s since 2015 = 223*9 + 8.
@Grim_Reaper @incelpardo99
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Correct
Let A be an n x n matrix with complex entries. If trace(AB)=0 for every n x n matrix B, show that A=0.
A
Suppose a_ij != 0. Let B = PD where P is a permutation matrix which will swap columns i & j of A and D is a diagonal matrix with d_ii = 1 and d_kk = 0 for k != i. Then AB will be nil save for column i, whose diagonal element will be a_ij. However, a_ij = tr(AB) = 0 is now a contradiction.
good job ! an elegant solution too. that problem is an old favorite of mine
A
It's a nice problem. I'll be assisting with linear algebra this quarter. Maybe I'll try to sneak in this problem.
damn youre living my dream
A
I hope you'll get there then. I also hope it'll bring you more joy than it does me. I'm currently getting a PhD but I don't see myself continuing in academia.
yea for now as a 3rd year undergrad academia seems like the move. but i imagine that may change once i actually see how brutal it is. i'll still try it out tho. i got nothing to lose
M
when you go asian, you never fail an equation
Amazing
A
My thoughts exactly at the timeyea for now as a 3rd year undergrad academia seems like the move. but i imagine that may change once i actually see how brutal it is. i'll still try it out tho. i got nothing to lose
I hate IQ moggers.
If you answered a correct question in this thread, you must be a sexhaver.
If you answered a correct question in this thread, you must be a sexhaver.
A
I'm too busy doing math to have sex
@Ahnfeltia probably has foid students asking him to give them better grades, and in-exchange they have sex with him.
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A
only happened thrice thus far
@IronsideCelonly happened thrice thus far
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