polynomial division vs simplify

by Miranda2829, May 25, 2025, 12:31 AM

the question is

4x² - 4x +1 divide by 2x + 1 write in fraction format

the answer is 2x-3 + 4/2x+1

so my question is can we simiplfy this -4x with 2x become -2x

then answer 4x² -2x+1?

Im confused , when do usual fraction division we can simplify, but in above question doesn't seem to work.

many thanks

Estimation Problems

by slightly_irrational, May 24, 2025, 10:39 PM

Is there a general strategy for problems like this where you find the first nonzero digit of some number?

Mathcounts 2025 Chapter Sprint 28
What is the first non-zero digit of $\sqrt{75^2 + 1}$ that appears after the decimal point?

Solve this

by DhruvJha, May 24, 2025, 9:20 PM

Len is playing a Arkansas-styled basketball game with his friend, Dawson. The game ends whenever a player has a 2 point lead over the other player. In Arkansas styled basketball, points can only be scored in increments of two. Whenever Len has possession of the ball, he scores at a rate of 60 percent. However, Dawson is slightly worse and when he has possession of the ball, he scores at a rate of only 40 percent. Given that Len starts with possession first each game, what is the expected amount of games he wins if they play 38 total?
This post has been edited 1 time. Last edited by DhruvJha, Yesterday at 9:22 PM
Reason: h
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Favorite topic

by A7456321, May 23, 2025, 11:53 PM

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What is your favorite math topic/subject?

If you don't know why you are here, go binge watch something!

If you forgot why you are here, go to a hospital! :)

If you know why you are here and have voted, maybe say why you picked the option that you picked in a response) :thumbup:

Timeline

Oh yeah and you see that little thumb in the top right corner? The one that upvotes when you press it? Yeah. Press it. Thaaaaaaaanks! :D
This post has been edited 3 times. Last edited by A7456321, Today at 2:52 AM

Tricky problem

by VivaanKam, May 23, 2025, 6:36 PM

$\text{Mrs. Lee announced that any student who scored }90\text{ or higher on the final test would receive an }A\text{ for the class.}$
$\text{Consider the following statements:}$

$\text{Lauren scored an }80\text{ on the final and received an }A\text{ for the class.}$
$\text{Lauren scored a }90\text{ on the final and received an }A\text{ for the class.}$
$\text{Lauren scored an }80\text{ on the final and did not receive an }A\text{ for the class.}$
$\text{Lauren scored a }90\text{ on the final and did not receive an }A\text{ for the class.}$

$\text{How many of the statements above are possibly true?}$

I got this problem wrong when I first tried it. :(
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Summer math contest prep

by Abby0618, May 22, 2025, 8:52 PM

School is almost out, so I have a lot of time in the summer. I want to be able to make DHR on AMC 8 in 7th grade

(current 6th grader) and hopefully get an average score in AMC 10. What should I do during the summer to achieve

these goals? For context, I have many books from AOPS, have already taken the Intro to Algebra A course, and took

AMC 8 for the first time as a 6th grader. If there are any challenging math problems you think would benefit learning,

please post them here. Thank you! :-D
This post has been edited 1 time. Last edited by Abby0618, May 22, 2025, 8:53 PM

khan academy

by Spacepandamath13, May 18, 2025, 11:27 PM

I haven't done khan academy in so long but today I had to learn law of sines. I wish khan academy taught competition math because their format, and self paced learning seems a bit better than aops' plus sal's videos for each topic are so good

Challenge: Make every number to 100 using 4 fours

by CJB19, May 15, 2025, 4:02 PM

I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
This post has been edited 4 times. Last edited by CJB19, May 17, 2025, 9:42 PM
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2025 Mathcounts Nationals Journal

by Andyluo, May 13, 2025, 4:43 PM

Friday May 9th

I spent my evening after school, packing for the trip, using the checklist given by my coach.
I didn’t do much preparation, as I was mostly chilling out for the upcoming days.

I also played basketball with my cousin, Kevin, who met Gotham Chess and stayed at his home!


Saturday, May 10th

I woke up at 5:30 AM, ate a light breakfast, and headed out to the airport with my luggage.

I met my teacher, but was surprised that Archishman split up with his own family.
Waiting for the TSA was pretty boring, but we soon got through, and after I found our gate.

A couple of minutes pass by, as I review an AOPS mock where I meet Archischman;
Afterward, we chill out, watch the rube goldberg machine in the airport, and wait to board the plane.

During the plane ride, I played games; however, during our descent, I heard a loud crack, and our plane started wobbling, and we heard cracking sounds in the seats. Fortunately, we were able to land and were able to attend the competition the next day.

After this, heading out, we went to the shuttle; however, we had 35 minutes. We tried to solve the Jane Street card puzzle but failed, and ended up socializing.

After we arrived at the hotel, we received a MASSIVE amount of stuff, like calculators, shirts, coupons, plaques, stickers, etc.
I also saw and got a signature from Richard Rusczyk, which was really cool.

Then, we went to a restaurant named “Chinatown Garden”, with the worst food I’ve ever had.

We then chilled in our rooms, studied for a bit, and started organizing plans for pin trading.

Our goal was to scam as many people as possible by doing 2:1 trades, as we had a “limited”
amount of pins. (We even got 5:1 and 10:1 trades)
A Virginia kid scammed me with a STEM pin, so I chased him down and got our pin back.

We got through around half the states organizing in and out of what pins we had.

Finally, we got some food from the buffet (which was surprisingly decent) and had a good time trading some more.

We ended the day with a short and brief CDR, where we had some fun, and then we went to sleep to anticipate the next day.

At night, I showered and sang karaoke with Archi.

Sunday, May 11th

Getting ready, I found out that a mock (outside the box) was recently released and took it through breakfast.

Then, once we got there at 8:30, there was a mob of parents taking pictures, and music played.

Then every team did introductions/attendance and their chants, most of which were really cringe.

I took the test; however was too slow on the sprint round and got a predicted 16.

On the target round, I was able to get through and got a 12, despite barely not solving p8 to my frustration.

Team round we did decently, scoring a 14/20, which was one of the best scores around us, that even orz states like Texas and Washington didn’t beat.

I predicted around a 28 with the answer key.

After this, we teamed up with North Carolina (chill af) and went to a pho shop (54 Restaurant), which tasted amazing. (A far contrast from Chinatown Garden)

Then, we went to an aerospace museum, where we played Brawl Stars and went around. Eventually, we saw models of blackholes and air vacuums, and played a flight simulator.

Then we went to our hotel, chilled, and watched basketball games.

After, we went to an Indian restaurant named “Himilayan Doko” which was really delicious!

Then we raided different rooms, from NC, HAWAII, Idaho, Virgin Islands, and accidentally a random dudes room who was ticked at us.

Finally, we chilled and went to sleep, though I tried to get Henry and Archi to sleep since they were being annoying.

Monday, May 12th

We start the day forming my pin badge, and then we went to get some breakfast.

After that, we met in the breakfast area with 2 teams for table, and I actually got a 10:1 pin trade which was pretty cool.

After that, we lined up and got our thunderstick/clapping machines, and ran through the entrance of the CDR.

Sadly, we didn’t win anything, but it was cool seeing the results.

Then, we started to watch the CDR, which was really exciting.
It got really interesting when everyone saw Nathan Liu cook his opponent in half a second.

In the semifinals, it was insane, and Advait and Nathan, buzzed every question that was around mid-sprint level.

Then, it finished with Nathan beating Brandon with a 2-second solve, absolute insanity.

Finally, we went back to our rooms and got lunch in the hotel.
A few hours later, we received our scores, and I had bombed, scoring a 26 with 7 sillies. (ouch)

Unfortunately, my teammates Henry and Archishman sillied a bunch of questions.

After, we played Brawl Stars, and went to explore the hotel, where we went up a random staircase and got stuck. We went to the roof, but got scared and yelled out for help on the gym floor. Thankfully, we got back, and I went and reviewed the test.

After we reviewed the test, and went to the Mathcounts Party.

The food was mid, but the games were pretty fun.

We met a bunch of people, played air hockey, foosball, and basketball, while listening to the not so great music in the background.

Then we went back to our rooms at 8PM, to put our pins on, and I got 38/56!

Finally, we met up in a room with a bunch of Cali, and NC kids, and talked about the test, the people, and played Brawl Stars. Even Josh Frost came up to us and asked us how the trip was.

Tuesday, May 13th

I started the day waking up at 6:20, and packed up and ate breakfast. After that, Henry was late, so we packed food for him and went to the bus shuttle.

Eventually, we arrived at the airport, went through security (which was suspiciously fast), and played Brawl Stars. We also ate five guys fries, which was pretty good. Eventually, we had to part our ways with Henry and headed out to our flights, which marked the end of the trip.

Conclusion:

Although we didn’t do amazingly well in the contest, going to DC was an amazing experience. I got to meet people who were passionate about math, and hang out with them, goofing around.

This was the best math contest experience that I’ll likely ever have, and I’m glad I went through it.
This post has been edited 2 times. Last edited by Andyluo, May 15, 2025, 12:00 AM

Phillips Exeter is looking for math kids! That means YOU!

by enya_yurself, Aug 9, 2024, 9:01 PM

I have received some insider information that may or may not prove to be helpful to you all. I am not sure where the best place to post this is, but somebody recommended msm so here I am.
Quote:
admissions was explicitly told to accept more math kids, 25 26 and 27 have been pretty disappointing for the math dept bc of covid
(source: a friend who talked to a faculty member on the admissions committee)

This means that Phillips Exeter is looking for more people like you all! I hope y'all choose to apply!

Remember that Exeter offers need blind financial aid :)

A guide to the science of secrecy

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fortenforge
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  • Good website!

    by bluegoose101, Aug 5, 2021, 6:28 PM

  • uh-huh, a great place here

    by fenchelfen, Sep 1, 2019, 11:30 AM

  • uh, yeah he is o_O

    by SonyWii, Oct 8, 2010, 2:11 PM

  • dude i think you're my roommate from camp :O

    by themorninglighttt, Aug 29, 2010, 10:06 PM

  • what i'm still not a contrib D:

    by SonyWii, Aug 6, 2010, 2:20 PM

  • I see what you did there

    by Jongy, Aug 1, 2010, 11:52 PM

  • omg, apparently you like cryptography; and apparently I'm not a contribb D:

    by SonyWii, Jul 26, 2010, 9:48 PM

  • Thank You

    by fortenforge, Jan 17, 2010, 6:35 PM

  • Wow this is a really cool blog

    by alkjash, Jan 16, 2010, 7:04 PM

  • Hi :)

    by fortenforge, Jan 7, 2010, 12:12 AM

  • Hi :)

    by Richard_Min, Jan 5, 2010, 9:29 PM

  • Hi :) :)

    by fortenforge, Jan 3, 2010, 10:14 PM

  • HELLO FORTENFORGE I AM THE PERSON SITTING NEXT TO YOU IN IDEAMATH

    by ButteredButNotEaten, Dec 24, 2009, 4:19 AM

  • @dragon96 Not if you celebrate Christmas with neon lights
    @batteredbutnotdefeated Sure, You are now a contributer

    by fortenforge, Dec 20, 2009, 4:39 AM

  • I too share a love for cryptography and cryptanalysis, may I be a contrib?

    by batteredbutnotdefeated, Dec 20, 2009, 2:38 AM

  • The green is too bright for Christmas. :P

    by dragon96, Dec 20, 2009, 2:12 AM

  • I thought I'd change the colors for the Holidays :lol:

    by fortenforge, Dec 13, 2009, 10:53 PM

  • hi, some "simple" cryptography here: http://www.artofproblemsolving.com/Forum/weblog_entry.php?t=317795

    by phiReKaLk6781, Dec 12, 2009, 3:46 AM

  • Yeah, that is binary, for modern cryptography, most text is converted to binary first and then algorithm's for encryption are preformed on the binary rather than the English letters. The text is converted using the ASCII table or UNICODE.

    by fortenforge, Oct 13, 2009, 10:33 PM

  • Whoa, I love your background! Is that binary?

    by pianogirl, Oct 13, 2009, 8:34 PM

  • Sure, I'll add you as a contributer...

    by fortenforge, Oct 2, 2009, 4:44 AM

  • May I make a post on one cipher I made up? (It's a good code for science people! *hint hint*)

    by dragon96, Oct 2, 2009, 4:04 AM

  • Nice blog, this is interesting... :lol:

    and guess who i am :ninja:

    by Yoshi, Sep 21, 2009, 4:02 AM

  • Thanks :lol:

    by fortenforge, Sep 17, 2009, 1:33 AM

  • Very interesting blog. Nice!

    by AIME15, Sep 16, 2009, 5:21 PM

  • When you mean 'write' do you mean like programming? Much of cryptography has to do with programming and most modern cryptographers are excellent programmers because modern complex ciphers are difficult to implement by hand.

    See if you can write a program for the substitution cipher. The user should be able to enter the key and the message. I know it is possible to do it in pretty much any language because I was able to do it in c.

    by fortenforge, Aug 7, 2009, 8:17 PM

  • Hello. I don't know much about advanced cryptography but I did write a Caeser Chipher encrypter and decrypter!

    by Poincare, Jul 31, 2009, 8:55 PM

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