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What is this sorcery?

Anonymous Tue 25 Aug 02:07:14 2020 No.12045306 View Reply Original Report

Quoted By: >>12045353 >>12045526 >>12045534 >>12046523 >>12046556 >>12046860 >>12046861 >>12046883 >>12046948 >>12047049 >>12047282 >>12047376

This originally started as a “math homework help request” that I made for my little brother, but no one I ask can help either online or in person so I just told him to go ask his teacher tomorrow what the hell this shit is.

So since it’s no longer homework help (like he already fell asleep anyway) I’m just completely dumbfounded by this math problem. I dropped out of HS so I could work, but it seems no one can solve this or explain how to solve it. So I thought I’d toss it over to you geniuses.

Anonymous

Anonymous Tue 25 Aug 2020 02:12:21 No.12045327 Report

Quoted By: >>12045351

Each function is a machine. Put 15 in for X, and then the result will go into the next machine. Which order of machines will produce -6?

Anonymous

Anonymous Tue 25 Aug 2020 02:20:22 No.12045351 Report

Quoted By:

>>12045327
Put 15 into one of the equations. Take that output, and drop it into the next equation. Repeat two more times. Seems like it would take some trial and error to have the final machine equal the proper output. I'm too lazy to bother.

Anonymous

Anonymous Tue 25 Aug 2020 02:20:25 No.12045353 Report

Quoted By: >>12045373

>>12045306
assign $f(x)=-2x+34 \\ <br />g(x)=\frac{-x}{3}-10 \\<br />h(x)=-|3x| \\<br />k(x)=(x-2)^2$
You want to find the order of these functions such that you take the output of one and input it into the next function's x, and when you put x=15 in for the first one the last one outputs -6.
Now it seems like there might be $4!=24$ ways of doing this, but because you know that the last output is negative, then $k(x)$ cannot be the last function (since its value is strictly positive). That reduces the number of possibilities to 18.

Similarly for b, you know that $h(x)$ cannot be the last function, since it is strictly negative.
It seems to me that this is largely guess-and-check beyond this.

Anonymous

Anonymous Tue 25 Aug 2020 02:27:05 No.12045372 Report

Quoted By:

looks like they are teaching composition of functions using the concept of "machines". I guess the metaphor is it's like an assembly line: every one of those 4 expressions takes in a part, processes it, and produces a modified part. In the metaphor, the part is the number you evaluate, so -2x+34 transforms "2" into "30", and so on. You can take the part from any machine and put it into another machine. The question is how do you connect the machines together such that putting "15" into the first machine and the assembly line spits out "-6" at the end.

The key insight, I suppose, is functions can be composed in the abstract sense:

if I have 2 functions:
x+2
3x-4

since a function just transforms x into an output, there's nothing stopping you from putting another function in where x goes:
3(x+2)-4
or the other way around:
(3x-4)+2

or an example without numbers: if I have 2 machines:
cut a block in half
drill a hole in it
I can describe the composite functions:
cut a (block with a hole drilled in it) in half
drill a hole in (a block that you cut in half)
You can see that this sort of substitution is equivalent to taking the output of one thing and using it as the input of another thing, in a series of steps.

Anonymous

Anonymous Tue 25 Aug 2020 02:27:19 No.12045373 Report

Quoted By:

>>12045353
adding to this, you can also intuit the order a little bit because some functions back-to-back will produce a huge number that has no way of really getting small enough to produce the desired outputs.
for example, if you started with k(x) and then applied h(x) (starting with 15), then you'd end up with -507. There's no way the other two functions can reduce this to -6, so you can eliminate this possibility.

Anonymous

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Anonymous Tue 25 Aug 2020 03:34:15 No.12045526 Report

Quoted By: >>12045529

>>12045306
didn't come up with a good general approach, but you can have this

Anonymous

Anonymous Tue 25 Aug 2020 03:35:19 No.12045529 Report

Quoted By: >>12046829

>>12045526
pretty sure there's not a general approach, you just have to use intuition to narrow down the possible solutions and a little bit of guesswork. maybe someone can prove me wrong

Anonymous

Anonymous Tue 25 Aug 2020 03:37:11 No.12045534 Report

Quoted By:

>>12045306
I dunno 4! or something

Anonymous

Anonymous Tue 25 Aug 2020 12:20:41 No.12046523 Report

Quoted By:

>>12045306
Those are some sick ass artifacts.

Anonymous

Anonymous Tue 25 Aug 2020 12:41:37 No.12046556 Report

Quoted By: >>12046591

>>12045306
Is the homework really just "brute force these functions a few times each. What's the point?

Anonymous

Anonymous Tue 25 Aug 2020 13:03:42 No.12046591 Report

Quoted By: >>12047063

>>12046556
I think the idea is that the students will demonstrate to themselves that composition of functions is non-commutative

Anonymous

Anonymous Tue 25 Aug 2020 13:16:07 No.12046623 Report

Quoted By:

Set x=-1 and everything will click.

Anonymous

Anonymous Tue 25 Aug 2020 14:38:32 No.12046829 Report

Quoted By:

>>12045529
Pretty stupid if that's the case, seems like a good way frustrate students.

Anonymous

Anonymous Tue 25 Aug 2020 14:52:54 No.12046860 Report

Quoted By:

>>12045306
There is no answer for the first. The last function must be -3x, and the one before it must produce a two. The two before that are questionable, but a brief survey
None of them work

Anonymous

Anonymous Tue 25 Aug 2020 14:52:57 No.12046861 Report

Quoted By:

>>12045306
smoking gun is the (x-2)^2. It can't be the last function, b/c it can't give a negative result. All the rest have to cater to that one.
Likewise, any f'n that needs a negative input to give -6 (the second one) can't come after the fourth.
Rest is probably just brute force

Anonymous

Anonymous Tue 25 Aug 2020 15:04:15 No.12046883 Report

Quoted By:

>>12045306
a. is 1-4-3-2
>15 -> (1) gives 4
>4 -> (4) gives 4 again
>4 -> (3) gives -12
>-12 -> (2) gives -6
(4) is trivial (disappears) when x=4, you could take advantage of that
(3-2) is trivial (function 3 disappears) when used in that order
b. is 3-2-4-1
>8 -> (3-2) gives -2
>-2 -> (4) gives 16
>16 -> (1) gives 2
just gotta keep your numbers small/integers and look for exploits

Anonymous

Anonymous Tue 25 Aug 2020 15:29:32 No.12046948 Report

Quoted By:

>>12045306
I used to like doing these puzzles as a kid. you can always apply the heuristic of "they probably made it nice numbers every step of the way" to inform your search order.

I can see it getting frustrating if you didn't use a heuristic and just tried brute forcing like a machine.

Anonymous

Anonymous Tue 25 Aug 2020 15:53:58 No.12047049 Report

Quoted By: >>12047282

>>12045306
There are 4! Combinations. Write a python script converting each formula to a function, make a list like so [‘a(x)’,’b(x)...]
Write a finction that takes a value x, and runs it through (via eval()) every permutation of the four functions recursively, then stores the sum of the function strings as keys with final output as value in a dictionary, or only save the one that outputs the correct answer.

Anonymous

Anonymous Tue 25 Aug 2020 15:58:20 No.12047063 Report

Quoted By:

>>12046591
Plus, it's getting them to play around plugging inputs into a few basic real functions to cement their understanding of how they behave, I guess.

Anonymous

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Anonymous Tue 25 Aug 2020 16:56:45 No.12047282 Report

Quoted By:

>>12047049
>>12045306

here you go anon

Anonymous

Anonymous Tue 25 Aug 2020 17:21:38 No.12047376 Report

Quoted By:

>>12045306
f(x) is one machine, g(x) is another.
f(g(x)) means you throw it through g(x), then pass the result through f(x).
Then you keep playing with order until you get out 15.
Meant to make it simpler for people that don't know maths. This is what happens when you set someone who loves maths to teach math illiterates.
Eventially someone will possibly get it right.

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