(just solving problems) i have very limited knowledge on the 500 formulas so i literally use guess + check, logic, creativity, and funny weird stuff that may or may not work for the problems.
this post is basically just to track my progress
to prove that i have been doing crap
besides i think organizing something with latex is really aesthetically pleasing and easier for me to review later

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problem 1 - 2022 amc 10b #13
question:
The positive difference between a pair of primes is equal to , and the positive difference between the cubes of the two primes is . What is the sum of the digits of the least prime that is greater than those two primes?
my solution:
first, i made a system of equations pretending that x=larger prime and y=smaller prime


then, i decided that it would be possible to substitute the x-y equation into the other one, so i tried this:
first factorizing

since x-y=2, you get plug that into the equation:
->
then, pretending that one prime is x and the other is x+2 (since it says in the problem that the positive difference between the primes is 2), you can substitute into the equation again
-> -> ->
[divide everything by 3]

[complete the square]
-> and 5184 nicely turns out to be a perfect square
[square root both sides]
which gets you or but since its the difference they are both positive so and (correct me on my logic flow here)
the next prime number is so you do and you get E (16) as your answer
overall: i'm sure there is a much simpler way to solve this, but then again i doubt my knowledge could support that. i'm using what i already know to just plug it in and although that is more time-consuming i doubt i can learn + comprehend new formulas 3 days before the amc.

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problem 2 - 2017 amc 10a #20
question: Let equal the sum of the digits of positive integer . For example, . For a particular positive integer , . Which of the following could be the value of ?
my solution:
i decided to use kind of the process of elimination for this one
A - for the digits to add up to one must be 99999... and is not a multiple of so we know this isn't correct
B - an example of a number that would work would be 20999 with the nine repeating because once you add one every nine cancels out and leaves one in the beginning so . isn't divisible by so we also know this is wrong
C - example of this would be like (eleven ones) and then the appropriate amount of 9's in the end. and this is not divisible by so it doesn't work
D - example is ones and then (once you add the one, the nines will cancel out and leave , and the digit addition difference is 35). (add one from the nines leaving the one once the is added) so you obtain D. so that's the correct answer
overall: i feel like this is a really wonky way to do it and that there's some super easy way to do it involving modular. i know some mod but i'm not comfy enough to implement it into these scenarios. again, i'm finding ridiculous ways to solve these problems that end up working but take some time. not so good for a fast-paced exam like the amc 10, but i guess it helps me use my brain and have some fun.

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questions i'm having trouble on: (i read the solutions but still dont understand so i need someone to dumb down for me)
2011 10b #16
2017 10a #19
2015 10b #17

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anyways this is for my practice and for smart people to judge me and be like what the hell is she doing why is she making it 500 times more complicated
the answer to that is i am simply not smart enough to know that my methods are really time consuming, but smart enough to know that the methods are kind of dumb
but if people could help me on the problems i'm stuck on that would be great
i heard c&p and especially geo are really important and unfortunately i suck butt at both of them