competition-math

[vestal silo]

wait lemme think

wait it’s not true that BD is a diameter

well

u can’t assume

[limpid shore]

The key is that ABCD is a cyclic quadrilateral

[vestal silo]

yeah but it could be a trapezoid

which is cyclic

iso**

[limpid shore]

The angles restrict that Yes you're right but it's not important

[limpid shore]

This means <DAC=<DBC=30 and <ACD=<ABD=45.

[vestal silo]

lemme think

[near hill]

It doesn't look like we have enough information. The central angle theorem tells us the relative positions of A, B, and C, but D could be anywhere on the arc between A and B without changing any of the angles.

Wait, no, I was reading the angles wrong. 🤦

[placid tapir]

[barren iron]

[hidden sigil]

is there any short way to solve it?

[jolly solstice]

I see a decent way of doing it by expanding the binomials and working through it that way, but may be better ways. I'll post my soln in a bit busy atm

[pallid dragon]

you get 10 from 3322 or 22222, there's no third way
there are 8!/2!/2!/4! ways to shuffle 33220000
there are 8!/5!/3! ways to shuffle 22222000
each of them makes 1x^10

so 476

[hidden sigil]

i will wait

0000?

the power

i see

[hidden sigil]

it is absoulety short and nice

let me apply it over another question

supoose we have
(1+x+x^2+x^3)

power is 2and we need to find x^4 coffi

i guess i am wrong somewehere

[pallid dragon]

the power is 5, so there's 5 numbers

or 2 if the power is 2

[hidden sigil]

sorry power is 2

wow

it is very very nice trick

it will be 3

[pallid dragon]

but that's one way as far as i understand, you can't say it's a trick

[hidden sigil]

one way?

i see

[pallid dragon]

the only way i meant

[hidden sigil]

can we apply it here

[pallid dragon]

i don't know sorry

[hidden sigil]

it is okay thanks

i will try

[jolly solstice]

you could expand out the (1-2x)^18 and just look at the first 4 terms as a polynomial, then you're only really looking at a few things multiplied together

$(1+ax+bx^2)(1+(-2)^1\binom{18}{1}x+(-2)^2\binom{18}{2}x^2+(-2)^3\binom{18}{3}x^3+(-2)^4\binom{18}{4}x^4)$

[gilded halo]

Mero

[jolly solstice]

x^4 term will just come from 3 terms multiplied, similarly for x^3 term

[hidden sigil]

tq very much

[idle fjord]

My sister (Rising 7th grader) is looking to get into comp math. Last year she scored a 12 on the AMC8. She can do basic algebra but nothing more, I gave her my old AOPS Vol 1: The Basics book but it was too hard for her.
Can someone send a list of AOPS books to do in order for her?

[acoustic nova]

AoPS pre algebra

[wanton bolt]

am I correctly interpreting this?

[limpid shore]

Yes the second equation is what you want to conclude

[wanton bolt]

got it, thx

[radiant jasper]

IF ANYONE CAN PLEASE HELP ME APPLE FOR AMC AUSTRALIAN I WOULD HIGHLY APPRECIATE IT 😭 😭 😭 😭 😭 😭 😭

[ornate blade]

you have to ask your school to enrol you

if your school doesn't offer the competition you can't join

[radiant jasper]

wait guys

@ornate blade

[ornate blade]

yeah

[radiant jasper]

my school did a math competition earlier this year

and they alr gave at awards

but on the website

it says its in AUGUST

[ornate blade]

https://www.amt.edu.au/amc yep

then what your school did wasn't the Australian one

maybe the American one, which is also called AMC

[radiant jasper]

OH

how can I tell if my skl does it

[ornate blade]

ask the maths teachers in your school

usually there's one maths teacher that runs all the maths competitions

[radiant jasper]

okay

this is what my school did @ornate blade

[radiant jasper]

wait if my school did the one above, would they likely do this one too?

[ornate blade]

it depends, they might or they might not

[radiant jasper]

ok if they are not

can I ask them to do it?

[ornate blade]

actually our school did a lot of competitions, the American one, Canadian, UKMT, and the Kangaroo one as well

but I had to take the Australian one outside of school

[radiant jasper]

how!

[ornate blade]

unfortunately the deadline to enrol in the paper-based test has already passed

[radiant jasper]

how do u do it outside of shcool

[radiant jasper]

can I do online

[ornate blade]

there was a maths club that organised it outside of my school

[ornate blade]

yeah of course

but then they would only let you do it online if they were your school

[radiant jasper]

dangit

😦

[ornate blade]

which leads me to believe that it isn't common to offer that competition

unfortunately

it's a nice competition, a lot like UKMT actually

nothing impossible

[radiant jasper]

are there any other comps this year

for aussies

[solar atlas]

whats 10+10 ?

[radiant jasper]

idk

[ornate blade]

not that I know of

[radiant jasper]

oh wait

[ornate blade]

like it really depends on what your school offers

[radiant jasper]

there is a thing

called ME

math enrichment

[ornate blade]

oh interesting

[radiant jasper]

if my school doesnt do it, can I request ?

[ornate blade]

yeah join that one, at least you can practice and socialise with other people with similar interests to you

[ornate blade]

yeah you can request

many Australian schools have some kind of enrichment due to gifted and high-achieving students

and maths is just such a common subject

[radiant jasper]

wait is the math enrichment like a test

or is it a course

[ornate blade]

no it's like an after-school club

or during lunchtime or something

[radiant jasper]

oh

there is another called

AIMO

[ornate blade]

oh AMT organises something of their own, interesting: https://www.amt.edu.au/enrichment

[ornate blade]

yeah I've heard of that one also

AIMO is actually from Hong Kong

oh wait there are 2 with the same name lmao

[radiant jasper]

bro all of this stuff is confusing

[ornate blade]

https://www.amt.edu.au/aimo

[radiant jasper]

so basically

should I Email my learning leader

[ornate blade]

ah so this is another Australian one I haven't heard of

but yeah it's like AIME just Australian it seems

[radiant jasper]

if they can do these math stuff

[ornate blade]

yeah

[radiant jasper]

wait what year level is u in

[ornate blade]

I'm at uni

doing a maths degree

[radiant jasper]

noice

NICE

im in year 8

[ornate blade]

oh nice

[radiant jasper]

I wish to do AIMO year 8

what are the topics?

[ornate blade]

yeah I'm at UofAdelaide if you wanted to know

[ornate blade]

they're on the website

[radiant jasper]

I mean it says this

[ornate blade]

May include:

Parallels
Similarity
Pythagoras’ theorem
Diophantine equations
Counting techniques
Expansion and factorisation
Inequalities
Sequences and series
Number bases
Methods of proof
Congruences
Circles and tangents
Probability

[radiant jasper]

but is it really like that?

[ornate blade]

there are sample papers

[radiant jasper]

cus like the first 3, inequalities, circle theorems, probability n stuff

bruhh my learning leader is doing smth at diff country

so she sent me an auto mailed

ig ill email when she bacj

[ornate blade]

yeah cool

[radiant jasper]

oh hell nah

[ornate blade]

it is school holidays in a big part of Australia also

[radiant jasper]

2017 is freaking impossible

[ornate blade]

so yeah just be patient

[radiant jasper]

bro is that like logarithms

[ornate blade]

oh no question 2 is about different number bases

so $2(b + 1)^2 + 3(b + 1) + 4$, that's what $234_{b + 1}$ means

[gilded halo]

southy

[ornate blade]

like you know how 234 in base 10 is shorthand for 2 * 100 + 3 * 10 + 4

same principle

[radiant jasper]

brother what are u spouting

[ornate blade]

probably stuff you don't know yet

but that's okay!

everyone has to start somewhere

[radiant jasper]

I mean I could just do all of them next year ig

[ornate blade]

yeah you have time yk

also not everyone who has the ability even needs to do Olympiad mathematics

that's just one very specific type of maths

I didn't enjoy competition maths all that much, well the initial rounds were fun but I didn't have interest in anything above that

[radiant jasper]

do you have any tips when test taking?

[ornate blade]

read and underline the question carefully, start off with the easier questions first (not necessarily the first few ones, maybe the middle ones)

don't get hung up on the last few hardest questions, if you can't do them that's very natural

also don't leave a question blank

time is a weird thing when doing competitions; it always seems like you never have enough

[radiant jasper]

Fr

Do you know how I could get some mathematics awards from anywhere

[ornate blade]

well a lot of it would be through your school

but check out GERRIC from UNSW, I did a winter mathematics enrichment course there in Year 7

https://www.unsw.edu.au/arts-design-architecture/our-schools/education/professional-learning/gerric-gifted-education/gifted-students-parents

[radiant jasper]

I live Melbourne

[ornate blade]

yeah

keep looking for opportunities I guess, I'm not exactly sure how much there is cause I didn't do high school in Aus

but given mathematics is so popular there's a huge demand for this kind of stuff

don't beat yourself up if you can't convince your parents to travel with you to Sydney

[ornate blade]

<@&268886789983436800>

[hidden sigil]

I learnt a method yesterday fir such questions

But why the method is not working

[hidden sigil]

Here

[pallid dragon]

in the previous exercise each way produced 1x^10, you need to pay attention to this

[pallid dragon]

221000
211100
111110

221000: 9 × −1 × 8 = −72
times 60, −4320
211100: 3 × −1 × 4 = −12
times 60, −720
111110: −1 × 2 = −2
times 6, −12

i get d

[hidden sigil]

I did not understand 9×-1×8?

And 60 times

[pallid dragon]

60 is 6!/2!/3!

3×3 gives 9, we multiply 3x² by 3x² so there's a 9

000 is 2×2×2 is 8

[hidden sigil]

Ohh ohhh

I missed coffiecients

Tq

[hidden sigil]

Is this cauchy schwarz?

[limpid shore]

||rearrangement inequality|| I believe

[acoustic nova]

yeah

[gilded halo]

shihgua
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[golden comet]

For nonnegative real numbers $a , b , c$ . How to show: $\frac{a + b + c}{3} - \sqrt[3]{abc} \leq \max {(\sqrt{a} - \sqrt{b})^2, (\sqrt{b} - \sqrt{c})^2, (\sqrt{c} - \sqrt{a})^2 $

[gilded halo]

shihgua

[velvet aurora]

this is Chebyshev’s inequality

[hidden sigil]

Yes

[gusty verge]

Perhaps do a WLOG proof, ie. Assume [(\sqrt{a}-\sqrt{b})^2\ge(\sqrt{b}-\sqrt{c})^2\ge(\sqrt{c}-\sqrt{a})^2]
As generally the maximum function is quite tricky to work with

[gilded halo]

Max

[velvet aurora]

I also suggest substituting [x^3=a, y^3=b, and z^3=c] to use the identity involving [x^3+y^3+z^3-3xyz]. I haven tried it, but it may help.

[quiet token]

I hate maths

[leaden herald]

very deep thought

[leaden herald]

333333

$\sum_{i=0}^{5} 3\cdot 10^i$

[gilded halo]

Rubix

[placid tapir]

Interesting

[leaden herald]

if somebody wants to know, I want to qualify for the national olympiad in my country

selection test is in March 2025, I hope I can get good enough by then

[limpid shore]

Gl

If your country isn't too hard you probably can

[leaden herald]

proofs are a relatively new concept to me though, I have to grasp them

[leaden herald]

Italy

it’s not too hard I think

[limpid shore]

yeah doesn't sound unreasonable

there are a few italians in the olympiads server, you could ask them for guidance

[leaden herald]

I’m not new to the olympiads, but I always participated with a team

I probably know some of them, if they’re gold medalists

know by name I mean

[limpid shore]

Idk if they're gold medalists

[limpid shore]

Does italy have many team competitions?

team competitions are really cool, i wish there were more

[ornate blade]

I mean why some countries do better on IMO than others is probably cause the other countries just don't care about competitions

[limpid shore]

• smaller populations

[ornate blade]

very true

[leaden herald]

there’s only one I’m aware of

which my school has participated in the last 7 years or so

[ornate blade]

also like many poor countries don't have the resources even if they tried

[leaden herald]

in the semi finals

[leaden herald]

India is an example

[ornate blade]

but yeah not relevant to Italy

[leaden herald]

all the good indian students study for jee

not olympiads

[ornate blade]

ah that's so true

[leaden herald]

it’s hard to organise stuff tho

plus nobody likes geometry

[limpid shore]

Some people do

🧐

[leaden herald]

I’m one of those who doesn’t study geometry for the olympiads, but if I want to get at least a bronze in the national, I have to

when I read the solutions I think some things are built out of nowhere

“draw the height of this small triangle AQK”, I would’ve never thought about that

[limpid shore]

yeah geometry is largely about good intuition for how things "should be"

[leaden herald]

I have some time

8 months

someone I know managed to get the bronze, starting pretty much from my same situation

so it’s not impossible

by the way, I’ll ask in the olympiad server, even though there’s not much to do, other than do many exercises

and understand the official solutions, if I can’t solve a problem

or if I can’t prove smth

[limpid shore]

Good mindset

Too many people get invested in learning theorems, tricks, etc.. when the key is just experience and doing a lot of problems

Nothing can replace that

And it's the most important ingredient

[leaden herald]

I’ve noticed that 90% of times I can’t finish an exercise because I can’t figure out the process, not because I don’t know a theorem

some things might help obviously

[limpid shore]

Yes exactly

[leaden herald]

like Vieta’s formulas and perfect squares mod 3 and mod 4

[limpid shore]

You wanna constantly be reflecting on the way you think to think to find out why you couldn't finish the problem

Learning from failure is extremely helpful

[leaden herald]

absolutely

for example I noticed that many times I forget restrictions, which can help me save a lot of time, by not trying all the cases

knowing the solution is an even prime tells you that it must be 2

but if you don’t put restrictions it’s way harder to notice

[willow anvil]

🤬🤬👺👺👺😡😡

[barren iron]

[radiant jasper]

No emphasis on geometry

[leaden herald]

the team is made of 7 people, and only one person actually wants to do geometry

😂

[pallid dragon]

the leftmost one

[willow anvil]

G>>>>>N>A>C

[crisp forum]

Has anyone ever felt guilty doing contest math problems? I enjoy them a lot more than traditional book problems but sometimes feel I should just be using the time doing contest problems to go further in higher levels of math.

[brave ocean]

I like geometry!

[fickle token]

I feel the same, it’s difficult because i feel like having good results from math competitions will also look good on college apps, but i’m just so much more interested in progress further in calc or diff equations than learning a bunch of random ways to factor polynomials that aren’t useful anywhere else other than competition-math. i set myself a goal by the end of high school to qualify for the AIME at least once, but it’s difficult to balance learning higher level math and competition math because of my specific interests.

[scarlet niche]

I love competition math! I made it to the national competition in MATHCOUNTS once and got like 15th place

[frosty nest]

yall

help

[novel karma]

simplify the equation first

[frosty nest]

fyi ive never tried anything like that

[novel karma]

wdym?

[frosty nest]

the type ofquestion

[novel karma]

put all the a's on one side of the equation

[frosty nest]

its for a competiton in august

[novel karma]

ok

do you need help or what

[frosty nest]

yes i do

[pallid tundra]

clear the fractions

[frosty nest]

alot of it

[novel karma]

yes

[frosty nest]

...

how exactly

[novel karma]

idk if this is comp math honestly lmao

try asking one of the help channels

[frosty nest]

im in 7th grade

if ur wondering

[novel karma]

so

[frosty nest]

idk

its from hakimo'

by ocec

[crisp forum]

That's interesting I'm the complete opposite where I enjoy learning weird theorems in geometry that are useful for Olympiad problems or other obscure tricks.

I also don't really know how helpful for college it is. I would say if you took say higher level courses at a college in highschool still that would probably look just as good or better.

[acoustic nova]

I feel like small branches of competition math like graph theory or game theory are a lot more interesting than like linear algebra. I don’t know linear algebra though so I’m just guessing but there is a lot of very cool competition math stuff (and these subjects are studied in detail outside of the competitions, ofc)

[brave ocean]

linear algebra is an extremely deep and rich subject

[acoustic nova]

yeah

I don’t know it doesn’t look as interesting to me but I’ve only seen very tiny pieces of it

[brave ocean]

which pieces have you seen?

[pallid tundra]

the stuff about vector spaces and linear maps

is a gateway into abstract algebra, analysis, etc

[acoustic nova]

matrix computations idk

a guy in one of my classes was giving a presentation on like end behavior of markov chains, that was interesting though

too hard for me to understand at the moment

[golden comet]

I have tried, but I only get the minimum zero!

[pallid tundra]

matrix computations are boring when they're unmotivated (describes the majority of high school and lower division undergrad treatments)

[leaden herald]

N>A>C>G

😭

[leaden herald]

if you plan on studying math at uni, that won't be a problem. They'll teach all you need, and if you have developed good logic skills that'll be easier

I've had this one week maths course at uni, it's completely different from what you're used to do in high school. An open mind is more important than learning things in advance

[jaunty fern]

Here, i could have written it better, but ive done it like this, ask if you have any questions

Im like 20 hours late but i joined this server an hour ago anyways

[scarlet root]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[near hill]

I don't think that applies with the same force here as it does when the problems are homework.
(@ivory ember)

[hidden sigil]

Anyone hints

[barren iron]

Left to the reader

[brave heron]

Interesting, I'm also competing in the same competition

[leaden herald]

def

it must be a lot of practice and that’s it

[barren iron]

Perfect makes practice

[sterile helm]

Does anyone here have a really good recommendation on how to prepare for math Olympiads?

And resources on how to do so?

[valid cairn]

depends on the level of the olympiad

but i really like the soviet olympiad book :]

https://archive.org/details/the-ussr-olympiad-problem-book-d.-o.-shklarsky/page/n5/mode/2up

theyre also helpfully categorised

[willow anvil]

Help

[sterile helm]

Thanks

I was wondering how can one learn all what is necessary for Olympiad. Let's say I just started Olympiad and wanted to get to a really high level. How would one do so? What resources are good for that?

[valid cairn]

again, it depends what level you want to achieve

high school Olympiad can be done with little more than simultaneous linear equations, or quadratic equations

of course you'll also need area/volume formulas but that's just an example

[sterile helm]

Alright thanks

[barren iron]

No problem

[upper knot]

Hey can anyone from australia give some insight on AMC if they have done it?

[brave heron]

amc you mean australian mathematic competition?

[upper knot]

yeah

[brave heron]

damn fast reply, I have an old copy of a 2017 senior a while back then, I joined one back then and I'd say it's kinda accurate on what will be part of the curriculum

[upper knot]

oh nice

[upper knot]

thanks

[brave heron]

it's a contest that goes progressively harder but it's possible to solve all in an hour, I suggest to focus most of your time on the harder ones first

[brave heron]

if you aim to do IMO level, you have to really spend like most of your time doing just math and practice your proving skills in all math curricula, especially when you live in a country with lots of competition

[valid cairn]

not a great competition overall

the questions are a lot easier than they need to be

additioonally, the timings are staggered and hence some people might have known then questions and potentially answers before going in

[brave heron]

that's more of an organizer issue I guess? but I do agree that it's easy compared to some non-IMO competitions out there

[valid cairn]

their questions are mostly brute-forceable

[brave heron]

yah plus most of the questions are multiple choice so it's really easy to cut off answers

[upper knot]

okok

i just thinking whether i should do it or not

[brave heron]

if you are a beginner, I think it's a great startup imo

[upper knot]

alright

[brave heron]

then just work your way up from harder stuff like joining your own local IMO team selection smth

you can even join despite being a beginner so you could get the feels

[upper knot]

is there any specific prerequisites that you think would be helpful like most common topics

[valid cairn]

just be familliar with the maths up to and including the year level of the competition

and some introductory discrete mathematics

[brave heron]

be a level advanced, if you are grade7, learn till quadratics, g8 learn till trigonometry

[upper knot]

year 9? quadratics, logarithms

i'm assuming

[ornate blade]

bruh WHY ARE SO MANY PEOPLE INTERESTED IN THIS ONE CONTEST

[brave heron]

one of the big contest organizers in my country hosts it sooo

[brave heron]

yup

[ornate blade]

oh interesting

[brave heron]

because grade 7 and 8 are all linear so you better advanced with quadratics at the start

[brave heron]

• it has its own wiki page too

[placid tapir]

Damn

That's cool

Interesting

[barren iron]

Engaging
Exciting

[noble scaffold]

pirate of the cartesian

omg

[placid tapir]

Ohhhhhh

[barren iron]

[ornate blade]

if I remove the p, will you be irate?

[barren iron]

Yes

[ornate blade]

lol

[acoustic nova]

no if u remove the pi he’s rate

[radiant jasper]

they will eat yummy foods in the future

[leaden herald]

I've tried a proof involving geometry right now: despite my proof being a bit more complicated than the official answer, I managed to get it completely correct

one step closer

I feel like I could get a medal at the national next year

I'm improving day by day

by the way I stumbled upon a combiantorics problem, and I can't really get out of it

Count all the $8$ letter words with the following properties: \
a) the word only contains the letters $A, B, C, D;$\
b) the letters $A, B, C, D$ must be used at least once;\
c) there are never two identical letters next to each other\

[gilded halo]

Rubix

[leaden herald]

my first idea was to count how many ways there are to put the $4$ forced letters $A, B, C, D$ in $8$ slots: $$\frac{8!}{4!}$$

[gilded halo]

Rubix

[leaden herald]

I can't get past this

[ivory ember]

ngl I'd just do PIE

four letters - three letters + two letters

[leaden herald]

does this include the third point?

no identical letters next to each other

[ivory ember]

third point is the entire reason why I chose a pie approach (since you can just pick the first letter and run w/ it for each of the three terms)

[leaden herald]

o lol

I'm still not the best

k lemme try

[ivory ember]

[leaden herald]

could you give me some more steps to solve that?

I can't figure out the solution

ok no let me try this one thing

no that's not it

[scarlet root]

Show your work, and if possible, explain where you are stuck.

[leaden herald]

ok

that's not really calculations, just logic

as I said before, since there are $4$ mandatory letters to insert, I've found in how many ways I can put them in a 8 letter word, and that'll be $$\frac{8!}{4!}$$
After that, I have $4$ empty spaces, that I have to fill accordingly, but by using PIE I'm not really considering everything. There could be a case with $5$ identical letters next to each other, for example: $$A B C D D D D D$$

[gilded halo]

Rubix

[leaden herald]

that step is not really clear

[leaden herald]

this

[ivory ember]

oh I kinda meant to just abandon this

ex. If there's 4 letters, then pick the first letter and consider how many ways there are to assign each of the following letters

[leaden herald]

that goes like

$$4 \cdot 3 \cdot 3 \cdot 3 \ldots$$

[gilded halo]

Rubix

[leaden herald]

the first letter can be chosen in 4 ways, the others in 3 ways

but not idk if there are all the letters I need, this could even be ABABABAB

[ivory ember]

hence why I did this

[leaden herald]

ohh

the four letter case will then be...

uh

[ivory ember]

didn't you just write it

[leaden herald]

4*3^7?

[ivory ember]

yeah

[leaden herald]

wouldn't it be

$$4 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 2 \cdot 1$$

[gilded halo]

Rubix

[leaden herald]

or...

[ivory ember]

you're assuming that you need to shove the other two letters in at the end

hence why I just did pie from the start

[leaden herald]

ok wait

the result turns out correct

:)

I'm still not sure why though

I'll have to think about it a lot

[leaden herald]

because

[ivory ember]

eh 4 * 3 * 2 * 1 * 3^4 -> order the first four letters and let the last 4 be whatever

but order would matter in a word

🤔

[leaden herald]

ye

$4 \cdot 3^7-4 \cdot 3 \cdot 2^7 + 6 \cdot 2 \cdot 1^7 = 7224$

which is indeed correct

[gilded halo]

Rubix

[leaden herald]

I might need a moment to think about it though

[ivory ember]

wdym as "correct"

,w 4 * 2 * 3^5

[gilded halo]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by civil_service_pigeon

[ivory ember]

as in 1944 is marked to be correct?

[leaden herald]

no?

[leaden herald]

this is what I did

[ivory ember]

ah ok I was gonna say

anyway I gtg

👋

[leaden herald]

alright

thanks for the help man

there's a lot to learn about the inclusion-exclusion principle

[vale pecan]

Umm

Is an average of 120 on the practice AMC 10 tests (former tests) a good score?

[sleek slate]

How former

[vale pecan]

From 2012-2023

Or 2024

Can't remember

AMC 10 a's and b's included

[vale pecan]

is that good?

[sleek slate]

Yea i think thats pretty good

U can easily qual aime with that fs but for usajmo/usamo ud need like a 10 to guarantee it unless its 2023s

[vale pecan]

you mean another 10 marks?

[vale pecan]

no worries 😄

thanks a lot

[sleek slate]

Nono like on the aime

Acc if it hits dhr then u need like an 8

[sleek slate]

Np

[vagrant mango]

is the info in the aops intro to geometry, intro to algebra, and intro to number theory enough to make aime?

[vale pecan]

So aime is 10/?

[vale pecan]

for the first 20 questions definetly

for the last 5 idk

[sleek slate]

oh out of 15

[sleek slate]

yes

[vale pecan]

all of them?

[sleek slate]

uh probs close but last 5 could be all over the place

[vale pecan]

how hard is that?

[sleek slate]

to qual u js need 100 so yea

[sleek slate]

first 10 rnt too bad then last 5 can be bad some years like 8-15 r pretty difficult but some years 1-10 r rly easy

[vale pecan]

oh

yay

[pallid tundra]

for pushing your abilities it helps to grind final fives

when test time gets close tho it’s strongly recommended to do full tests under test conditions

[vale pecan]

oh

When I have like 30%-40% probability of getting a question right do I leave it blank or write my answer?

cuz the competition's i've been in give no marks for unanswered questions (except gauss, which can't say much as the questions are all answerable)

[pallid tundra]

if guessing isn’t punished its better to just put something down

doesn’t apply to competitions like the AMC 10/12 tho

[hidden sigil]

hints please

[gilded halo]

Rubix

[leaden herald]

no idea, but at least it's readable now :)

[vague maple]

Help i can't figure this out

[barren iron]

[silk gazelle]

Hey guys, can you kindly help me out here, i accidentally passed my first comp and idk what to do for next round, this is a practice question from their previous previous year but i have no clue on how to solve it, thank you so much :)

[ornate blade]

they seem to have a really elegant method but I don't know how to do it

anyways you can just use the cosine rule, so $\cos z = \frac{116 + 370 - 74}{2 \sqrt{116} \sqrt{370}}$

[gilded halo]

southy

[silk gazelle]

I dont think calculator is allowed thats why im asking here

😢

[ornate blade]

I know I'm not sure what they mean

by their hint

[ornate blade]

but it's doable by hand actually

just don't simplify the sqrt(116) sqrt(370)

the answer is 11 somehow

basically in the sin z = sqrt(1 - cos^2 z) part of the calculation

you need to do 116 * 370 - 206^2

ugly but it evaluates to 484 = 22^2

so $\sin z = \frac{22}{\sqrt{116} \sqrt{370}}$ and hence the formula $\frac{1}{2} ab \sin C$ gives $\frac{1}{2} \frac{22}{\sqrt{116} \sqrt{370}} \sqrt{116} \sqrt{370}$

[gilded halo]

southy

[ornate blade]

there's always more than one method in maths

[silk gazelle]

It is 11 from the answer sheet i js dk the way :'D

[silk gazelle]

Hmm i understand 1/2 ab sinC but thats all i understabd

[ornate blade]

ok that's something at least

[ornate blade]

okay then (116 + 370 - 74)/2 = 206 right

we're simplifying cos z a bit

[silk gazelle]

Yeaa

[ornate blade]

and then $\sin z = \sqrt{1 - \left( \frac{206}{\sqrt{116} \sqrt{370}} \right)^2 }$

[gilded halo]

southy

[ornate blade]

= $\sqrt{\frac{116 \cdot 370}{116 \cdot 370} - \frac{206^2}{116 \cdot 370}}$

[gilded halo]

southy

[ornate blade]

so that's how we need to do 116 * 370 - 206^2

[silk gazelle]

I see

But why do we need to get 206

Im sorry im a bit slow 😭

[ornate blade]

all we are saying is that $\cos z = \frac{206}{\sqrt{116} \sqrt{370}}$

[gilded halo]

southy

[ornate blade]

we just divided the 2 into the numerator

[ornate blade]

that's the same as this

[silk gazelle]

Hmm

Ahh its from cosine rule?

[ornate blade]

oh RIGHT yeah it is the cosine rule

yeah ok that makes sense that you were stuck there

so the side lengths are already squared

so to find XY instead of XY^2 we need to square root

[ornate blade]

yes

[silk gazelle]

I see

[red stream]

Hello. Has anyone done any of the problems from the mathematical reflection journal? Here is the link of the problems: https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2024-03/mr_3_2024_problems_2.pdf. I would really appreciate if one of you guys have solved or could solve one of the problems for me.

[barren iron]

[brave heron]

WOAH SIMOC

[silk gazelle]

I gave up

[brave heron]

if you want a more psychotic solution, you could express each side as a, b, and c, and you could apply herons formula for that, you would have to multiply 4 trinomials but it would end in a satisfying way such that all terms are squared, then you could use the given options

[silk gazelle]

Im trying to understand southy's explanation but im still confused as where 22² come from

[silk gazelle]

I tried herons because my friend requested it and it turns to

I dont think i did it right

Sorry its messy 😭😭

[brave heron]

it would be easier to express it as a b and c

it should end like this and just substitute

[silk gazelle]

I accidnetally passed amo with just bronze and now my mom put me in so idk whattodo now😢

[brave heron]

you would want to get the last part, the one with the a^4 etc

it should be viable but yeh, using trig is probably much better

[silk gazelle]

Ahhh

[silk gazelle]

I think so too

Im trying to digest this information

[brave heron]

what category?

[brave heron]

it's a question 25 anyway, it's fine, I'm pretty sure simoc is like 2 hours from what I know

[brave heron]

nvm its 90 but expanding that 4 trinomials is kinda easy cause of the lack of coefficients and also, a lot of things will cancel out

[silk gazelle]

IDK 😭😭the math one..???

[brave heron]

I mean as a secondary 1, 2 , 3 , 4, SS?

[silk gazelle]

Sec 4

[brave heron]

oh wow, i'm younger than you by 1 secondary

[silk gazelle]

😭that was my first comp idk what to do

[brave heron]

are you singaporean?

[silk gazelle]

No im not😢😢

[brave heron]

damn you're going onsite

[ornate blade]

I considered Heron's at first but I realised that would be insane

like you have to find s

then subtract everything and ehhhh

[ornate blade]

you'd have to know the 3rd form here ye

I don't think that's realistic to memorise

[silk gazelle]

Yea i did it substituting as x but then i remember i need to put x back in 💀

[ornate blade]

but yeah like if it's openbook then absolutely just do this

[brave heron]

OH YEAH THIS

it's a one way shortcut tbh, with easy derivation

kinda like sophie germain

[ornate blade]

yeah

people already did the algebra for you to get it into that form

[brave heron]

just familiarize yourself with a lots of concepts, I like AMO and SASMO because its kinda similar to AMC 10 and 12

[silk gazelle]

OH I JUST ASKED MY.. UHH JUNIOR FRIND

He found a way

Without cosine and allat

With just.. drawing triangles

We tried that before but we draw the triangle wrong and he found a way for the correct triangel using the hints

Holy

[brave heron]

let me see

[ornate blade]

oh that's nice!

yeah I'm curious now

[silk gazelle]

Waiy ill redraw his triangle

[ornate blade]

okok

[pallid tundra]

there’s a proof I’ve seen that just uses Pythagoras a few times

for heron

[ornate blade]

https://en.wikipedia.org/wiki/Heron's_formula#Algebraic_proof_using_the_Pythagorean_theorem

this one?

[silk gazelle]

OHHMY

THEN FROM THAT ON JTS JUST FINDING AREAS AND SIMPLE MATH

[ornate blade]

,rotate

[ornate blade]

SHIT it's that simple

I should have drawn it

[silk gazelle]

HOW DOES BRO THINK OF THAT

AND HES LIKE UHH GR 8 LAST YEAR

[ornate blade]

,calc 1/2 (17 * 9 - 10 * 4 - 7 * 5) - 4 * 7

[gilded halo]

Result:

11

[ornate blade]

I think they were just willing to try

I was lazy to try it on pen and paper

typing is easier for me

[silk gazelle]

😭😭

[brave heron]

hold on, i don't see it what

[silk gazelle]

I drew triangles too but wromg ones

Actually ive thought of that but never thought the triangle will be lookin like that

[silk gazelle]

Also very not to scale sorry for bad drawung💀💀

[brave heron]

i'm so clearly lost

[silk gazelle]

dude just saved me from stress wth

It was that easy?? Omg

[brave heron]

ok I get it now

okay that's actually genius

[silk gazelle]

Right!! I never thought of that, i thought of shapes before but i was only thinking how to make a rectangle work

[brave heron]

geometry is my so so weakness

[silk gazelle]

Never thought it was actually a bigger triangle

[pallid tundra]

first step of any geometry problem

draw a diagram!

[brave heron]

you now have 3 possible methods for this, shows how most maths are interconnected

[silk gazelle]

:D math is so interesting but so frustrating sometimes abhahaha i have love hate relatiobship with math

[radiant jasper]

for reall

[silk gazelle]

But once you actually solved just that 1 question you feel like everything is

So cool and stuff

This is the most ridiculous question ive encountered

[radiant jasper]

yeaa but i love how every thing is connected in it and how everything is so significant

[silk gazelle]

I dont think this is even maths

[brave heron]

yah especially geometry is so frustrating where most questions can't be solved with just drawing triangles(you have to learn about this obscure theorem to solve it)

[silk gazelle]

😭😢

[silk gazelle]

What was the question makers thinkin abt when creating this question.. pity points for those who cant math? (me)

[radiant jasper]

it must have to do someting with SnS right?

[brave heron]

I had a math contest question during G7 which can be solved using stewarts theorem and I only learned it during G8

[radiant jasper]

or is it higher maths?

[silk gazelle]

Whats sns

[radiant jasper]

Sequence and series

[silk gazelle]

No its so funny i found it in a sec thats why i called it ridiculous

[silk gazelle]

Its simpler than that

You dont even need to think abt maths

[radiant jasper]

then tell us the logic🤔

[silk gazelle]

Think like a kindergartener and u probably find it

[silk gazelle]

Look at dem holes in the numbers

[brave heron]

man what

[ocean narwhal]

Thats dumb

[silk gazelle]

Exactly!!

[brave heron]

is that simoc?

[silk gazelle]

I think so idk

[radiant jasper]

ewww😂

[silk gazelle]

SEE

Thats why i called it ridiculous

[radiant jasper]

i didn'teven thought that far lol

[vestal silo]

this is terrible

[brave heron]

if you solve this riddle, you are smarter than 99.99% type question

[silk gazelle]

I thought of that first time (i have the brain of a 6 yo)

😭😭😭

[silk gazelle]

Ikr

[brave heron]

I was thinking modulo but that 0 to 1 doesnt make sense

[silk gazelle]

BAHAHHA 😭😭😭 THOSE NONSENSE QUESTIONS ARE LIKE SOMETIMES SNEAKED IN IDK WHY

[radiant jasper]

umm i have a problem? with determinants using factor theorem

[silk gazelle]

Thinking too far

[vestal silo]

I thought it was some weird series for the left col

[ocean narwhal]

I was thinking( how many ways can you write the number a product of primes) - 1, treating 0 as an exception

[silk gazelle]

No its just batshit nonsense 💀💀

[vestal silo]

You could map a polynomial on the left

[radiant jasper]

what is the logic behind second point?

[silk gazelle]

Yall r too smart for this wtf 😭😭 i did it first try because im dumbfounded with the other questions hellkkpfnm

[ocean narwhal]

Thatd actually make so much sense

[vestal silo]

#precalculus , or maybe #linear-algebra

[radiant jasper]

me as well

[vestal silo]

not really 💀

[radiant jasper]

okay

[ocean narwhal]

Way better than looking at holes.

[vestal silo]

i do agree!

[silk gazelle]

BAHAHAHAHAH I AGREE

Who put that question in that i wanna talk to the creator of that question

[brave heron]

my sasmo book had some of that nonsense

[silk gazelle]

LOL

[ocean narwhal]

Report them to the proper authorities if you find them

[brave heron]

"logical reasoning"

[ocean narwhal]

Id not expect that shit to pop in a math quiz thats for sure

[silk gazelle]

😂😂😂but no logic

[silk gazelle]

Reall

[brave heron]

gl with that simoc stuff

I think they just put that on the kindergarten stuff instead of the higher level category, if they did have logic questions, it's probably more reasonable than the amount of holes in a number

[silk gazelle]

Tyy

Also ty to southy for helping :D

[silk gazelle]

i think they should too

[pallid tundra]

cooking up an absolutely computationally evil geo problem

😁

unfortunately I can’t share it here bc I plan to put it on a math contest this fall

[brave heron]

consider studying trigo solutions because most of the time, there might be a trigonometric solution

[silk gazelle]

Alright! Also where could i find math resources to study from?? :)

[brave heron]

I use youtube and some aops, in simoc there's also a syllabus for that

[silk gazelle]

Whats aops??

Ohhh apps?

[brave heron]

nooo

art of problem solving

theres a lot of amc aime type questions there with solutions\

then a lot of concepts too

[pallid tundra]

their books are pretty good

even if the problems tend to be a bit dated difficulty wise

[brave heron]

large forum and even had a lot of solutions too for imo problems and other countries selection test

[brave heron]

yah, I recommend buying Vol 1 and Vol 2 if you did consider joining a lot, but there are a lot of resources too especially for a contest like simoc since it doesnt use much higher forms of math

[silk gazelle]

Ahhh is that a book?

[silk gazelle]

I see

Ty yall

:)

[pallid tundra]

npnp

[brave heron]

it's an organization

it has a website too

[pallid tundra]

I applied to intern with them this summer but someone else had already taken the spot 😭😭

next year I guess

[brave heron]

damn lucky, you must have been an experienced olympian

[pallid tundra]

I was never that good 💀💀

only ever made AIME once, barely

but I have a good deal of experience writing problems

[silk gazelle]

Okk lemme searcgh

[pallid tundra]

aops.com

[silk gazelle]

How do u get experience help all i joined is noob competitions and i still cant do them because skill issue

I basically join random she that my school offers, thank god some dont have them... selections thingys😭😭

Im not that smart to begin with either

[silk gazelle]

Tysmm

[brave heron]

well start a lot of noob competitions, that's how I started too when I was G7, now I qualify for an area stage for imo selection in my country(I'm still bad tbh,will try again this year)

[silk gazelle]

Wow thats so good thoo

Im so far away from that

How do you practice??

[brave heron]

a lot of practice from other materials + having a clique in your school would help a lot too, I asked a lot during my G7 to my other smarter seniors and that gave a lot of insights as well

solve easy ones

then solve harder ones, if you can't understand the concept, you can search for the concepts behind it and use that too

sometimes I use the alcumus of aops to solve specific topics

most questions from that came from existing AMC 12 and other existing contest, which is fun

nawh its free, just make an aops account

you can even do cauchy schwarz here which is kinda funny

[ornate blade]

hint (spoilered!):
||a + 4b + 9c = 16
4a + 9b + 16c = 25
9a + 16b + 25c = 36

a = 1, b = -3, c = 3||

[silk gazelle]

Tyy! I do agree having friends to help r rly useful and im grateful that i do :)

[ornate blade]

oh basically that's the same technique

so then we want $a(x_1) + b(4x_1) + c(9x_1) = 16x_1$

and so on

[gilded halo]

southy

[ornate blade]

also we do have to show that $n^2 - 3(n + 1)^2 + 3(n + 2)^2 = (n + 3)^2$ to make sure the pattern holds

[gilded halo]

southy

[delicate basin]

lol south i just joined this and you're here 😭

[ornate blade]

lol

yeah and you only need 3 equations cause that's enough to figure out if there is one solution or not

there shouldn't be infinitely many solutions given the setup of the problem

[brave heron]

Theres a much more fun solution there tbh

Well not really fun but satisfying

Found it by dumb luck

[ornate blade]

oh is it on AOPS

wait but I don't have the year or the source

[brave heron]

Idk

[delicate basin]

people how the hell do you practice for amc10 😭

i did 1 practice test and im pretty happy with how it turned out (91.5) but idk where to start.. the difficulty seems to go up enormously at the end

[ornate blade]

you're in the right place my man

[delicate basin]

i thought i wouldn't be able to do it because of school but nevermind i found out that time zones are not shooting me in the head for once

[brave heron]

But you can set the 16x1 + 25x2 as equation 4 as S

X1 + 4x2 .. = 1 as equation 1
4x1 + 9x2 .. = 12 as equation 2
9x1 + 16x2.. = 123 as equation 3

Then subtract 1 from 2, 2 from 3 and 3 from 4

To get eq 5 as 3x1 + 5x2 ...= 11
Then eq 6 as 5x1 + 7x2... = 111
Then eq 7 as 7x1 + 9x2 ... = S - 123

Then just subtract eq 5 from 6 and eq 6 from 7

To get 2x1 + 2x2 + 2x3 etc in both eq 8 and 9 which has 100 and S - 234 each, you can find S as 100 = S - 234 then S = 334

[ornate blade]

oh wow that's an amazing method

yeah so I convinced myself with $5x_1 - 3x_1 = 2x_1$ and $7x_1 - 5x_1 = 2x_1$

[gilded halo]

southy

[ornate blade]

so yeah second difference constant implies that

[ornate blade]

same as what Vanellope did haha

,calc 3(123-12)+1

[gilded halo]

Result:

334

[brave heron]

I'm on my smartphone and I don't know how to use LaTex sorry

[barren iron]

$$a^2+b^2=c^2$$

[gilded halo]

πrate of the Cartesian

[brave heron]

I realize since the second difference is constant. One could just take advantage of the difference of the sums [1,12,123,S] and branch them out, one could get the first differences [1,111,S-123] instead, then second differences [100,S-234] then get S as 334.

1 minute solution

Ultrasimplified version

[delicate basin]

ppl how the hell do you revise for amc10??

i did 1 practice test and im pretty happy with how it turned out (91.5) but idk where to start.. the difficulty seems to go up enormously at the end

[pallid tundra]

for problems you didn’t get correct, read over the solutions

final fives being hard is deliberate by design

[delicate basin]

on my practice I didn’t even attempt the last 6

but there’s all kinds of stuff that it seems I just have to.. know

like the modular arithmetic

[pallid tundra]

focus on maximizing your score on earlier questions first

91.5 is not a safe score for AIME qual

the late questions will tend to throw a lot of more obscure techniques at you

[delicate basin]

definitely not lmao 😭

[pallid tundra]

if you can get, say, the first 15 locked down

[delicate basin]

Do you know why the average score has gone up lately?

[pallid tundra]

then you’ll be in a very good position

[delicate basin]

I checked and it went from like 5x to 6x

[pallid tundra]

test difficulty? fewer people taking it?

I haven’t looked at the last few years’ tests lmao

[delicate basin]

On my practice I got 12/15 of those right, skipped 2, got 1 wrong cuz im silly 😭

[delicate basin]

do you know what’s a good score to aim for that’s actually realistic

[pallid tundra]

with how low cutoffs have gotten

105+ is probably sufficient

[delicate basin]

and also how do I practice this kind of stuff again

[delicate basin]

out of interest do you know if universities care about this kind of thing

[pallid tundra]

not unless you get far

say, USAMO+

[delicate basin]

ah 💀

so they don’t care about aime 😭😭

ill still try to get there

[pallid tundra]

the big names don’t particularly care about AIME

but outside that bubble it could give you an edge in admissions

[delicate basin]

ah

well

i wasn’t thinking too deep into amc

but now i realize that i am quite literally like 2 or 3 problems off aime so I want to try

[pallid tundra]

yea

[leaden herald]

this year I've decided to focus on math olympiads just to prove to myself that I can do it

in Italy no university cares, except maybe Scuola Normale Superiore (SNS) in Pisa (probably the best university for math in the world)

[leaden herald]

all throughout high school I've never felt challenged by standard math questions, that's why I'm pushing higher

[delicate basin]

good point :)

[delicate basin]

really!

i was focusing more on harder exams instead of Olympiads

(which are.. much easier to prepare for lol)

the number theory and geometry especially on amc is giving me a headache

[leaden herald]

well if you don't compete at IMO level you can pretty much forget entering that uni

[leaden herald]

number theory is quite hard

there are a lot of disconnected things to remember

[delicate basin]

oops

[leaden herald]

here's one I've learnt some days ago

[delicate basin]

it’s very basic number theory and it’s still confusing me

[leaden herald]

a perfect square $s$ is either $\equiv 1 \pmod{3}$ or $\equiv 1 \pmod{4}$

[gilded halo]

Rubix

[delicate basin]

Hmm

[leaden herald]

this is so random to me, but extremely useful

[delicate basin]

oh wait that’s actually

interesting

the proof is probably 2 years long or something

[near hill]

144 is neither.

[delicate basin]

ohhh

[leaden herald]

.. true

but I've read that somewhere

or probably I remember it wrong

probably it was either 0 or 1 mod 3 and mod 4

[near hill]

Yeah, that would be correct.

[leaden herald]

here we go

right now I'm solving problems on the inclusion- exclusion principle

[delicate basin]

i did a bit of digging

[leaden herald]

it seems to be fundamental in competitions

[delicate basin]

what the hell are these theorems

“chicken McNugget theorem”

😭🙏

[leaden herald]

lmao

[delicate basin]

it’s literally needed

for an amc10B problem

[leaden herald]

pigeonhole principle

[shrewd girder]

pigeonhole principle might be the MVP of contest math problems ngl

[near hill]

It's slightly more dignified to call it the "Frobenius coin problem".

[shrewd girder]

Yeah

[leaden herald]

I've never read a solution stating "by the pigeonhole principle"

[delicate basin]

https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_15

aops themselves called it

chicken mcnugget theorem

[leaden herald]

but probably I've read some saying "since we have more elements than there are spaces" or things like that

[willow anvil]

php has been overshadowed by global

[delicate basin]

😭😭

[shrewd girder]

i say it sometimes just to convey the idea of whats being done but its the principle behind it

i mean the statement of it seems glaringly obvious

but

its a really powerful way of thinking

[leaden herald]

yea I realised

[near hill]

Well, the goal for contest preparation is not to be dignified, but to be memorable.

[shrewd girder]

https://en.wikipedia.org/wiki/Coin_problem#McNugget_numbers

LOL

McNugget numbers

[shrewd girder]

That and also if he wants to look into it further + related stuff he'll probably be better off calling it coin problem instead

when looking it up

[leaden herald]

this year we had a team competition, and our "jolly" problem literally was:

How many non-empty subsets of ${1,2,\ldots,13}$ there are, so that the product of their elements ends with $0$ ?

this is inclusion exclusion basically

(ps. we couldn't solve it, although it's not really hard)

[gilded halo]

Rubix

[leaden herald]

this morning I was lost, but I've tried a few exercises and I'm getting it

still not competition level, they're just generic PIE exercises

[shrewd girder]

imnot looking yet cause im gonna take a stab at it soon myself

||yeah that was my thought, like total is the size of the powerset and then subtract out the ones that don't at least one of both 2 and 5 in the factorization||

i just can't write out atm

[jolly bridge]

||i think that might be missing a -1 because it specifies non-empty subsets||

||but then it gets un-accounted for in 2^6||

[gilded halo]

Vanellope von Schmugz

[pallid tundra]

hint: symmetry

[sterile helm]

Does anyone know how to do 90^2+56^2 really fast without calculator?

ok np

because in the solution I'm reading they went from 90^2+56^2=106^2 and in the test you cannot use a calculator

oh

how would u know that

what if I only knew a and b?

that will be tough without a calculator lol

oky

[brave heron]

I'm willing to bet this is 2023 AIME I Problem 5

[brave heron]

This is just 28 45 53 so you could take advantage of that

[rough dock]

anyone got resources to practice/learn on for someone who’s new to this level of math?

[acoustic nova]

yeah

[brave heron]

Art of problem solving. The whole website is great

[rough dock]

thanks! does it have solutions and all the theory stuff too?

[brave heron]

Yes(well if you searched the topic itself, I think) but the theory stuff does show up, and most of their problems had lots of solution from AMC to AIME to USAMO and Even IMO

[rough dock]

ok, thanks so much

[barren iron]

Keep asking

[hidden sigil]

66

B and C option are same?

I guess c is correct

[leaden herald]

it is

[leaden herald]

it somehow cancels out

the actual solution is 2^13-1-(2^11-1+2^6), and, guess what, they cancel out

[fading bluff]

88?

they aren't same

[hidden sigil]

Yeah

[fading bluff]

(a.b)= -c.a

[brave heron]

Nawh obviously

My math teacher sent me stuff who is part of the wide connection of the deputy team leader of my country who is with the contestant

[brave heron]

For 1, obviously a case is all even integers but idk how to prove the others

I'll probably just get max 3 points by claiming that it's probably even integers(but hey atleast its a point)

[brave heron]

I saw this on aops, I don't really get how case 2 and 3 works

it's all even though(great)

[brave heron]

i'm so cooked, till now I only have even integers case

[brave heron]

was it 54?

i hate these problems about constant rate stuff

I agree

where did 33 come from

how is that a hint?!

ohhhhhh

my bad

I guess you could express this algebraically

from what I see on the internet, the 54 notion had a LOT of assumptions

[gilded halo]

Vanellope von Schmugz

[snow dirge]

BTW the time she leave the school on normal day is 4PM?

1 hour head start = 12 mins early?

[brave heron]

yuh

[snow dirge]

Also the velocity of the girl walking during the school-station and station-home isn't the same?[

SRY to make this more complicated 🤣

[brave heron]

exactly, too much reliance on whatever

[snow dirge]

what is 33 doing here anyway LMAO

[snow dirge]

another question from me. Normally, when the girl reaches the station, does she meet her mother and get on the car immediately?

Or should I assume this one in my calculation for first of all?

[brave heron]

that's actually the supposed assumption to get 54

[snow dirge]

Ok ty

[snow dirge]

This is my simulation on Scratch. I created 2 sprites which represents the girl on normal day(cat) and on special day(woman). I set the time ratio by 1:600 as the picture below. The total distance is 480 units from school to house. Velocity on foot and by car are also mentioned.

The second picture describes that on special day she got picked up on the way between the station and house at x=60 which is a quarter distance to home.

[placid tapir]

Scratch scratch

[snow dirge]

But I made some mistakes there.

1. As you can see the time for the cat should have started after he began to move.
2. Both of the timer should have stop when they began to move faster(on car).

Yeah that’s what I thought 😂😂

It’s impossible to solve this problem without knowing the velocity.

Smash, next pls🤣

[zealous violet]

whats a good way to study for amc 10s?

ive been doing practice tests but cant seem to get my score up

[brave heron]

damn NNN GCA

best year in imo for someone who's geometry is their weakest

[brave heron]

OKAY P5 IS ACTUALLY REALLY EASY OMG

THE ANSWER IS THREE

The trick is to determine to location of the monster in the second row

if the monster is not on the edge, one should start at either adjacent of the monster, and go down and go to the direction behind the monster, worst case scenario, you die on your second attempt(bad luck) then you could just respawn easily on the other adjacent

if its on the edge, create a staircase like path starting adjacent on the monster then go left(or right) instead of down first(because its a 2024 by 2023 not a square), the go down left/right, down, left/right, till you either finish it or not, if you didnt, there are two cases, if the monster is encountered when you go left or right, then just go in the opposite direction till you got to the edge where monster 1 is encountered, if the monster is encountered when you go down, one shold take a step back in a row and not go left/right and just go double down and go in the opposite direction till you got to the edge

OMG P5 SOLVED in 20 MINS

why is it so easy

they screwed up(I think)

if a hobo like me who struggles at some low level competitions yet can solve a P5 in IMO then we are done

[zealous violet]

anyone got study tips for the amc 10/12?

so far ive been doing practice tests and tutoring sessions but they dont really seem to stick

i have heard that keeping a small notebook with formulas is a good idea, so I started to do that

but i was wondering what else I could do to boost my scores