State target p8 sol

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EaZ_Shadow

1229 posts

EaZ_Shadow

#1 h Apr 6, 2025, 3:53 PM • 3 Y

Y by PikaPika999, Soupboy0, jkim0656

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

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greenplanet2050

1312 posts

greenplanet2050

#2 h Apr 6, 2025, 3:55 PM • 1 Y

Y by PikaPika999

ikr i literally kinda guessed this one correct

This post has been edited 1 time. Last edited by greenplanet2050, Apr 6, 2025, 3:55 PM

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EaZ_Shadow

1229 posts

EaZ_Shadow

#3 h Apr 6, 2025, 3:56 PM • 1 Y

Y by PikaPika999

greenplanet2050 wrote:

ikr i literally kinda guessed this one correct

Lowk mathcounts was def cooking with that sol!

This post has been edited 1 time. Last edited by EaZ_Shadow, Apr 6, 2025, 3:56 PM

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evt917

2335 posts

evt917

#4 h Apr 6, 2025, 3:56 PM • 1 Y

Y by PikaPika999

i didn't take mathcounts cuz i'm only in 5th grade

but i also checked the problems

the solution was way too good

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DreamineYT

282 posts

DreamineYT

#5 h Apr 6, 2025, 4:01 PM • 1 Y

Y by PikaPika999

EaZ_Shadow wrote:

This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!

our team got p1 team wrong :noo:

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sadas123

1228 posts

sadas123

#7 h Apr 6, 2025, 7:39 PM • 1 Y

Y by PikaPika999

It is actually a good solution and I am not being sarcastic skull

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maxamc

549 posts

maxamc

#8 h Apr 6, 2025, 7:47 PM • 1 Y

Y by PikaPika999

i did all 10 team round in 19 min but failed target p8 and i am not being sarcastic skull

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sadas123

1228 posts

sadas123

#9 h Apr 6, 2025, 8:19 PM • 1 Y

Y by PikaPika999

maxamc wrote:

i did all 10 team round in 19 min but failed target p8 and i am not being sarcastic skull

skull i did 11 team rounds and got a perfect on target and sprint to get 46 overall ¿como estas?

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DottedCaculator

7337 posts

DottedCaculator

#10 h Apr 6, 2025, 8:41 PM • 3 Y

Y by PikaPika999, jkim0656, scannose

https://www.eecs.qmul.ac.uk/~norman/papers/probability_puzzles/equal_sequences.shtml

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maxamc

549 posts

maxamc

#11 h Apr 6, 2025, 9:03 PM • 1 Y

Y by PikaPika999

DottedCaculator wrote:

https://www.eecs.qmul.ac.uk/~norman/papers/probability_puzzles/equal_sequences.shtml

https://www.youtube.com/watch?v=t8xqMxlZz9Y

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huajun78

64 posts

huajun78

#12 h Apr 6, 2025, 9:44 PM • 1 Y

Y by PikaPika999

Quote:

The probability of getting consecutive coin tosses with the pattern HTT is (2/3)(1/3)(1/3)=2/27 . The expectation value of the number of tosses needed to first achieve that pattern is the reciprocal of that probability, thus 27/2.

I don't get the solution (why can you just reciprocate it?)

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Craftybutterfly

383 posts

Craftybutterfly

#13 h Apr 6, 2025, 9:51 PM • 1 Y

Y by PikaPika999

Is MATHCOUNTS only for middle school students or also high school students or elementary students as well?

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DottedCaculator

7337 posts

DottedCaculator

#14 h Apr 6, 2025, 9:56 PM • 4 Y

Y by PikaPika999, huajun78, iwastedmyusername, vincentwant

huajun78 wrote:

Quote:

The probability of getting consecutive coin tosses with the pattern HTT is (2/3)(1/3)(1/3)=2/27 . The expectation value of the number of tosses needed to first achieve that pattern is the reciprocal of that probability, thus 27/2.

I don't get the solution (why can you just reciprocate it?)

Consider doing many coin tosses. Each appearance of HTT is disjoint, and the total number of HTTs is 2/27 times the number of tosses, so the expected distance to the next one is 27/2.

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mdk2013

611 posts

mdk2013

#15 h Apr 7, 2025, 12:19 AM

Y by

i did it like dottedcaculator did, everyone was like did you p8 and they were like god that problem was actually hard, and i was like bruh its just that the probability is 2/3*1/3*1/3= 2/27 so the expected number is 27/2 lol you guys shouldve seen my friends expression when i told him that

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scrabbler94

7553 posts

scrabbler94

#16 h Apr 7, 2025, 12:27 AM

Y by

DottedCaculator wrote:

Consider doing many coin tosses. Each appearance of HTT is disjoint, and the total number of HTTs is 2/27 times the number of tosses, so the expected distance to the next one is 27/2.

I like how this solution fails if HTT is replaced with, say, TT. The expected number of flips is not 4 in this case.

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andrewmao1221

16 posts

andrewmao1221

#106 h Apr 16, 2025, 12:18 PM

Y by

What you mean 2 diagrams? I think here the second situation applies. Then this becomes the easiest 8th question. The probability of HTT happen is: 2/3*1/3*1/3=2/27. Thus the expected number of trials is 27/2.

However, I think the question is kinda of wrong. Here the expected number of trials is not the expected number of flipping. The trial includes 3 flipping. At least, the question should make it more clearly what it is asking about.

This post has been edited 1 time. Last edited by andrewmao1221, Apr 16, 2025, 12:29 PM
Reason: Additional thoughts

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Craftybutterfly

383 posts

Craftybutterfly

#108 h Apr 16, 2025, 3:05 PM

Y by

Why do you have to reciprocate the fraction?

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andrewmao1221

16 posts

andrewmao1221

#109 h Apr 16, 2025, 3:26 PM

Y by

A previous post derived the equation why $E(X)=\frac{1}{p}$ . A simple intuition is:
Let $m$ be the number of trials for you to get one success. $m\times p=1$ . Thus: $m=\frac{1}{p}$ . An even simpler intuition: If you do something with a success rate of 0.2, how many times on average will you have to do so you get one success? Oh, it is 5. How do you get it? 1/0.2

Craftybutterfly wrote:

Why do you have to reciprocate the fraction?

This post has been edited 2 times. Last edited by andrewmao1221, Apr 16, 2025, 3:33 PM
Reason: typo

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pingpongmerrily

3567 posts

pingpongmerrily

#110 h Apr 16, 2025, 6:14 PM

Y by

MC_ADe wrote:

States is a really good way to go about but realizing that after using CRT for p7 you won't have time to use states on p8 was kind of sadge

bro you don't need CRT for p7
its just like basic lcm work

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derekwang2048

1225 posts

derekwang2048

#111 h Apr 16, 2025, 6:52 PM

Y by

wait i just grinded units digit
and then added 40 i think, even if you use crt it is the most basic form (0, 1, 2)

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Andyluo

929 posts

Andyluo

#112 h Apr 16, 2025, 10:26 PM

Y by

dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

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Aaronjudgeisgoat

894 posts

Aaronjudgeisgoat

#113 h Apr 17, 2025, 12:38 AM • 2 Y

Y by RollingPanda4616, c_double_sharp

i thought the world was experiencing inflation, so why are the quality of problems in contests going down

This post has been edited 1 time. Last edited by Aaronjudgeisgoat, Apr 17, 2025, 12:38 AM

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Soupboy0

336 posts

Soupboy0

#114 h Apr 17, 2025, 1:37 PM

Y by

bc why not

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K1mchi_

68 posts

K1mchi_

#115 h Apr 17, 2025, 1:39 PM

Y by

Aaronjudgeisgoat wrote:

i thought the world was experiencing inflation, so why are the quality of problems in contests going down

quality is going down bc test writers cant keep up w inflation

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mulberrykid

122 posts

mulberrykid

#116 h Apr 17, 2025, 3:08 PM

Y by

nothing is wrong with the solution, no whining about it. Not true for HHH but good for HHT.

Andyluo wrote:

dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

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Craftybutterfly

383 posts

Craftybutterfly

#117 h Apr 17, 2025, 3:09 PM

Y by

Aaronjudgeisgoat wrote:

i thought the world was experiencing inflation, so why are the quality of problems in contests going down

2025 AMC 8 is significantly easier so as 2024 AMC 10

This post has been edited 1 time. Last edited by Craftybutterfly, Apr 17, 2025, 3:09 PM
Reason: :D

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RollingPanda4616

220 posts

RollingPanda4616

#118 h Apr 17, 2025, 3:32 PM

Y by

Aaronjudgeisgoat wrote:

i thought the world was experiencing inflation, so why are the quality of problems in contests going down

skimpflation!

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UberPiggy

35 posts

UberPiggy

#119 h Apr 17, 2025, 5:15 PM

Y by

mulberrykid wrote:

nothing is wrong with the solution, no whining about it. Not true for HHH but good for HHT.

Andyluo wrote:

dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

But that's the thing: if it using reciprocals works for HHT but not HHH, that means it does not work universally. It is most likely that MathCounts tried to use an incorrect shortcut that coincidentally ended up giving the same answer.

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Craftybutterfly

383 posts

Craftybutterfly

#120 h Apr 18, 2025, 4:58 AM

Y by

Andyluo wrote:

dottedcalculator, an 2x imo gold medalist has told me that the solution is wrong.

The only real solution is using states, which can be found on the AOPS mathjam

https://artofproblemsolving.com/school/mathjams-transcripts?id=716

have i been scammed

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derekwang2048

1225 posts

derekwang2048

#121 h Apr 18, 2025, 5:26 PM

Y by

yes.
but it is also dottedcaculator not dottedcalculator

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