STATE SOLUTIONS AND STUFF DROPPED!!!

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Soupboy0

322 posts

Soupboy0

#1 h Apr 4, 2025, 5:44 PM

Y by

https://www.mathcounts.org/resources/past-competitions

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Soupboy0

322 posts

Soupboy0

#2 h Apr 4, 2025, 5:45 PM • 2 Y

Y by megarnie, PikaPika999

wait actually i think its about to drop MATHCOUNTS just has not finished replacing the PDFs

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jb2015007

1862 posts

jb2015007

#3 h Apr 4, 2025, 6:04 PM • 1 Y

Y by PikaPika999

YES ITS OUT FINALLY

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jb2015007

1862 posts

jb2015007

#4 h Apr 4, 2025, 6:04 PM • 1 Y

Y by PikaPika999

bruh i added wrong on 24 and 25

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c_double_sharp

307 posts

c_double_sharp

#5 h Apr 4, 2025, 6:07 PM • 1 Y

Y by PikaPika999

s11 was dumb i added wrong
s18 was dumb how did i not see that
s23 was dumb how did i not see that
s24 was dumb how am i not able to read properly
s27 was dumb like the official solution was assume rectangle
t6 was dumb like i did not calcbash enough terms
t8 was dumb how did i not see that

This post has been edited 1 time. Last edited by c_double_sharp, Apr 4, 2025, 6:07 PM

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MathPerson12321

3697 posts

MathPerson12321

#6 h Apr 4, 2025, 6:23 PM • 1 Y

Y by PikaPika999

c_double_sharp wrote:

s11 was dumb i added wrong
s18 was dumb how did i not see that
s23 was dumb how did i not see that
s24 was dumb how am i not able to read properly
s27 was dumb like the official solution was assume rectangle
t6 was dumb like i did not calcbash enough terms
t8 was dumb how did i not see that

totally agree

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iwastedmyusername

78 posts

iwastedmyusername

#7 h Apr 4, 2025, 7:24 PM • 3 Y

Y by MathPerson12321, PikaPika999, mithu542

wth is the explanation for t8

Attachments:

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jb2015007

1862 posts

jb2015007

#8 h Apr 4, 2025, 7:32 PM • 1 Y

Y by PikaPika999

ikr mc quality has dropped so much this past year

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MathPerson12321

3697 posts

MathPerson12321

#9 h Apr 4, 2025, 7:56 PM • 1 Y

Y by PikaPika999

iwastedmyusername wrote:

wth is the explanation for t8

ikr

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Soupboy0

322 posts

Soupboy0

#10 h Apr 4, 2025, 7:57 PM

Y by

bro why does mathcounts coordbash 90% of geo problems

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maxamc

542 posts

maxamc

#11 h Apr 4, 2025, 8:18 PM

Y by

c_double_sharp wrote:

s11 was dumb i added wrong
s18 was dumb how did i not see that
s23 was dumb how did i not see that
s24 was dumb how am i not able to read properly
s27 was dumb like the official solution was assume rectangle
t6 was dumb like i did not calcbash enough terms
t8 was dumb how did i not see that

I also assume rectangle because I hate rigorous geometry

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PuppyPenguinDolphin

1323 posts

PuppyPenguinDolphin

#12 h Apr 4, 2025, 8:30 PM

Y by

iwastedmyusername wrote:

wth is the explanation for t8

Can someone explain why the expectation is the reciprocal?

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Eddie_tiger

336 posts

Eddie_tiger

#13 h Apr 4, 2025, 9:06 PM • 1 Y

Y by PuppyPenguinDolphin

PuppyPenguinDolphin wrote:

iwastedmyusername wrote:

wth is the explanation for t8

Can someone explain why the expectation is the reciprocal?

I think it’s because 2/27 is the probability of having the set, and expected value is just 1/p. You will need to memorize that E = 1/p

This post has been edited 1 time. Last edited by Eddie_tiger, Apr 4, 2025, 9:06 PM

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SpeedCuber7

1801 posts

SpeedCuber7

#14 h Apr 4, 2025, 9:22 PM

Y by

Eddie_tiger wrote:

PuppyPenguinDolphin wrote:

iwastedmyusername wrote:

wth is the explanation for t8

Can someone explain why the expectation is the reciprocal?

I think it’s because 2/27 is the probability of having the set, and expected value is just 1/p. You will need to memorize that E = 1/p

this post does a very good job of explaining why $E = \frac1p$

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Owen314159

12 posts

Owen314159

#15 h Apr 4, 2025, 9:24 PM • 1 Y

Y by PuppyPenguinDolphin

PuppyPenguinDolphin wrote:

iwastedmyusername wrote:

wth is the explanation for t8

Can someone explain why the expectation is the reciprocal?

Because it's kind of like saying it has a $2$ in $27$ chance of happening, so it happens twice every $27$ times. This means that it is expected to happen once every $27/2$ times.

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Soupboy0

322 posts

Soupboy0

#40 h Apr 5, 2025, 1:08 PM

Y by

i memorized sprint 20 before the competition:skull:

This post has been edited 1 time. Last edited by Soupboy0, Apr 5, 2025, 1:09 PM

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MathPerson12321

3697 posts

MathPerson12321

#41 h Apr 5, 2025, 3:12 PM

Y by

@3above correct, this works for one time things and mostly is an intro to expected value.

You have to consider the other factors as well.

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superhuman233

473 posts

superhuman233

#42 h Apr 5, 2025, 5:59 PM

Y by

i was so lucky that i guessed sprint 20 right otherwise i wouldn't have made nats

Click to reveal hidden text

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ilikemath247365

243 posts

ilikemath247365

#43 h Apr 5, 2025, 6:00 PM

Y by

Bro, sprint 20 took the most time for me in the first 20. I can't believe that I actually did coordinate geometry on the real test on this problem!

I also almost trolled this problem. I miscalculated by somehow getting the square root of 49/25 but I clutched and caught my mistake to change it to the square root of 81/25 which is 9/5.

This post has been edited 1 time. Last edited by ilikemath247365, Apr 5, 2025, 6:01 PM

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Andyluo

920 posts

Andyluo

#44 h Apr 5, 2025, 6:02 PM

Y by

superhuman233 wrote:

i was so lucky that i guessed sprint 20 right otherwise i wouldn't have made nats

Click to reveal hidden text

how is that guessing lmao, it's how you're supposed to solve it. honestly belongs in first 10 questions

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jb2015007

1862 posts

jb2015007

#45 h Apr 5, 2025, 6:16 PM • 1 Y

Y by PikaPika999

20 was didnt take too long for me
js had to draw the altitude and do some coord bashing then pythag then ur done

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JamesYMath

12 posts

JamesYMath

#46 h Apr 6, 2025, 12:34 AM • 1 Y

Y by PikaPika999

You could've also used the altitude theorem for #20 but I guess that's just similar triangles

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PikaPika999

1151 posts

PikaPika999

#47 h Apr 6, 2025, 12:44 AM

Y by

MathPerson12321 wrote:

c_double_sharp wrote:

s11 was dumb i added wrong
s18 was dumb how did i not see that
s23 was dumb how did i not see that
s24 was dumb how am i not able to read properly
s27 was dumb like the official solution was assume rectangle
t6 was dumb like i did not calcbash enough terms
t8 was dumb how did i not see that

totally agree

fr tho

This post has been edited 1 time. Last edited by PikaPika999, Apr 6, 2025, 12:44 AM

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giratina3

492 posts

giratina3

#48 h Apr 6, 2025, 1:44 AM • 1 Y

Y by PikaPika999

I choked #7 on sprint because I thought for some stupid reason that the maximum area of a triangle with perimeter 24 was a right triangle :wallbash:

Probably could have gone to nationals with that question. Just saying...

Sigh... guess I just wasn't able to make nationals because I'm too nervous during the test... which is exactly what happened last year too.

So close to nationals... yet so far...

This post has been edited 1 time. Last edited by giratina3, Apr 6, 2025, 1:45 AM

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martianrunner

155 posts

martianrunner

#49 h Apr 7, 2025, 4:17 AM

Y by

i had seen some extremely trivial solution for p4 target that didn't even require a calculator but i forgot it now

does anyone have a non-bash solution for that one

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derekwang2048

1219 posts

derekwang2048

#50 h Apr 7, 2025, 4:23 AM

Y by

i just solved the system of equations and it was pretty straightforward, i realized how to do it with like 2 minutes left

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Bummer12345

132 posts

Bummer12345

#51 h Apr 7, 2025, 1:01 PM

Y by

martianrunner wrote:

i had seen some extremely trivial solution for p4 target that didn't even require a calculator but i forgot it now

does anyone have a non-bash solution for that one

here are 5 stupid solutions to target #4

sol 1 (sort of bash, most logical)

sol 2 (cheese, no bash)

sol 3 (graphing calc)

sol 4 (even more cheese)

sol 5 (sol 2+3 equals 5)

This post has been edited 3 times. Last edited by Bummer12345, Apr 7, 2025, 1:09 PM
Reason: latex

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c_double_sharp

307 posts

c_double_sharp

#52 h Apr 7, 2025, 1:31 PM • 1 Y

Y by MathPerson12321

p8 is 27/2 confirmed but why does the official solution work

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happypi31415

742 posts

happypi31415

#53 h Apr 7, 2025, 4:48 PM • 2 Y

Y by Aaronjudgeisgoat, MathPerson12321

The official solution works because the coins follow a Binomial Distribution, which means that we have that $E[x]=np$ where $E[x]$ is the expected value, $p$ is the probability, and $n$ is the number of trials. This also follows from linearity of expectation on each of the groups of $3$ . Then, setting $E[x]=1$ and $p=\frac{2}{27}$ gives the desired answer.

Alternatively, another easy solution is to use recursion: suppose that we want the expected number of rolls, $x$ , until an event happens with probability $p$ . Then, we have that $x=p+(x+1)(1-p)$ which rearranges to the desired $x=\frac{1}{p}$ .

edit: thinking about it now im not completely sure this is valid because expected amount of rolls between HTH and TTT is different but whatever

This post has been edited 3 times. Last edited by happypi31415, Apr 7, 2025, 8:32 PM

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fruitmonster97

2467 posts

fruitmonster97

#54 h Apr 7, 2025, 5:29 PM

Y by

target seems interesting
personal difficulty ratings: 1 is trivial, 10 is nats t8(from a year not named 2024 or 2023)
t1: 1, trivial, just average 9876 and 5432.
t2: 1.5 to 2, trivial but annoying.
First two seem hard to silly, esp. with 1 being so easy.
t3: 1 to 1.5, also trivial.
t4: 2 to 2.5, too easy for the placement.
Another very sweepable round, as intended. Nowhere near the difficulty of last year's t4(which was the only one i got wrong last year).
t5: 1 to 1.5, just floor(202/24)
t6: 6 to 7, imo perfect placement. nontrivial. Albeit you don't even have to find the intended solution, simply approximate 2^2025-1 to 2^2025 and plugging the first ~13 terms into a calc should give a good approximation.
t7: 3 to 3.5, fair placement. simple crt.
t8: 4 to 9, really just depends on your perception. there are definitely people who just assumed you can always reciprocate, but there are definitely people who tried much, much harder methods.

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