one nice

by teomihai, Aug 2, 2025, 4:55 PM

Without compute the sum: $S=2+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}$
find the nearest whole number to $S$.

Make the numbers 1-100 using 1-100 1-100s

by ZMB038, Aug 2, 2025, 4:29 PM

So in this game we try to make the n th number with n copies of n. For example make 9 with 9 9s. Hope you guys enjoy.


Edit: no using add subtract multiply or divide more than once.
L

Sixseven!

by fossasor, Aug 2, 2025, 4:17 AM

A sixseven-ish pair consists of two integers from one through ten such that the two integers and the sum of their lengths when written out, in some order, form an arithmetic sequence with a non-zero difference. For example, (obviosuly) six-seven is one such pair: six has 3 letters and seven has 5 letters, combining to make 8 letters, and 6, 7, and 8 form an arithmetic sequence of length one. However, three-ten is not a sixseven-ish pair, since 3, 8, and 10 do not form an arithmetic sequence in any order. The order of these numbers does not matter, so sixseven and sevensix. for example are considered the same.

1. There are only five pairs of sixsevenish numbers, and sixseven is one of them. What are the other four?

2. Alice wants to find the five pairs of sixsevenish numbers (she knows the fact that there are only five of them) and she knows that no number from one to ten, when written out, has a length of greater than five or less than one. However, Alice only speaks Brainrot, in which the numbers have different lengths, so she doesn't know the length of any number when written out. However, she has a magic LeMelo machine - when asked if a pair of numbers is sixseven-ish and given a quarter, it will tell her whether or not the numbers are sixseven-ish. Using logic, what is the minimum number of cases Alice has to check to prove that the five pairs are the only sixseven-ish numbers? Keep in mind that this proof should not rely on our knowledge of number lengths - if all the numbers had different lengths within these bounds, it should still function. (Finding the minimum is difficult - I do not have an answer to this problem, but I have an upper bound.)
This post has been edited 3 times. Last edited by fossasor, 2 hours ago
L

Alice and Bob

by PTV, Aug 2, 2025, 2:24 AM

why do literally like 90% of comp math questions have the characters Alice and Bob???? especially on mathcounts and amc 8, they overuse these people. like js pick someone else for once bro, like what the sigma??? its not like the ceo of maa is gonna crash out if the problem writers choose different characters bruh


4TH POST LETS GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
This post has been edited 1 time. Last edited by PTV, Today at 2:25 AM
Reason: I mistyped something

Can you outsmart the clock

by Merkane, Aug 1, 2025, 3:20 AM

The King of a small country invites 1000 senators to his annual party. As a tradition, each senator brings the King a bottle of wine. Soon after, the Queen discovers that one of the senators is trying to assassinate the King by giving him a bottle of poisoned wine. Unfortunately, they do not know which senator, nor which bottle of wine is poisoned, and the poison is completely indiscernible. However, the King has 10 prisoners he plans to execute. He decides to use them as taste testers to determine which bottle of wine contains the poison. The poison when taken has no effect on the prisoner until exactly 24 hours later when the infected prisoner suddenly dies. The King needs to determine which bottle of wine is poisoned so that the festivities can continue as planned. However, he has time for only one round of testing. How can the King administer the wine to the prisoners to ensure that he is guaranteed to have found the poisoned wine bottle?

This problem elegantly demonstrates how mathematical thinking and logical reasoning can be used to extract precise information under extreme constraints. It invites us to think not only creatively, but systematically — making the most out of limited opportunities. I'm curious to see how others might tackle it; I’ll share my solution after a day.

need new mathcounts mock tests

by Ynsg, Jul 31, 2025, 10:22 PM

I am trying to make mathcounts nationals next year and I've kinda been falling off with speed and accuracy while I've been studying new topics. I think I should mock tests, but I've pretty much done every mathcounts state and national test from 2000ish up till 2024 once or twice. where can I find a consistent source of mock tests that I can use at least until the end of summer or some other solution?

A tale of dragons - demo

by ethanhansummerfun, Jul 31, 2025, 4:36 AM

This is a part of a series that I’ve been working on. If y’all like this type of problem I can publish the whole set.

4. In the land of $\sqrt{-1}$, the continent is divided into $10$ regions, as shown. Dragon island, far in the northeast, has just birthed $12$ dragolings. Dragolings are very territorial. Any dragoling next to another one of the same element will immediately attempt to annihilate one another and lay waste to the entire continent. You must assign each dragoling to its own region. Adjacent sides are NOT ok, but touching corners are. An old master informs you just before you convene your council that an extremely rare wind dragoling may be coming. He informs you that it must have one ice, fire, AND lightning adjacent to it or else it will be bored and also destroy the whole continent. Dismissing it as a myth, your council informs you that you have enough power to create $2$ new regions by cutting any already existing region in half by connecting points not adjacent to each other such that the line drawn passes through exactly $1$ region. As you ask your scouts what they saw, you realize in horror that they said they scouted $4$ fire, $4$ ice, $3$ lightning, and $1$ mysterious white dragon, the legendary wind dragon. This is not a Zelda reference even though my pfp says otherwise.

You have 10 minutes. (not really) Which 2 regions should you bisect to save the continent?
Attachments:

Theorems for AMC 10 later problems

by R.Mathphile, Jul 27, 2025, 5:21 PM

Hi I'm looking for theormes for Amc10 problems (preferbaly used in question 18 and after) geometry is also preferred
Also If someone has any tips from going to getting a 5 on aime and 115 on amc 10 to going to USAJMO please tell me
Anyways thx for your time :)

6-7 number pairs

by hellohi321, Jul 27, 2025, 1:16 AM

Define a 6-7 number pair to be a pair of consecutive positive integers such that when read out loud one after another, you hear the phrase "six seven". For example, 76, 77 is a 6-7 number pair since it is pronounced "seventy-six seventy-seven". Find a closed form for the number of 6-7 pairs in which both terms are less than $10^n$

Sorry if this has a lot of brainrot lol. I thought of this while listening to brainrotted kids as a summer volunteer

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  • The aura

    by centslordm, May 12, 2025, 8:05 PM

  • same, luckyleaf

    by MightySpider, Mar 31, 2025, 4:06 AM

  • woah this blog is older than me lol
    nice blog! :coolspeak:

    by luckyleaf77, Jan 11, 2025, 3:20 PM

  • admits
    ed

    by sixoneeight, Aug 10, 2024, 12:13 AM

  • https://artofproblemsolving.com/community/c3841395

    by Rename, Jul 21, 2024, 3:12 PM

  • wow cool blog! :D

    by BakedPotato66, Jan 10, 2024, 2:27 AM

  • Awesome!

    by Neurotricity, Oct 20, 2022, 9:38 AM

  • Can I be contrib? Thanks!

    by MC413551, Oct 8, 2022, 2:14 PM

  • Very nice blog :)

    by programmeruser, Sep 19, 2022, 12:23 PM

  • Wow! this is EPIC!

    by mathkid369, Jul 11, 2022, 2:43 PM

  • This blog is amazing! I've found so much useful information on here. Thank you!

    by je100, Mar 25, 2022, 5:04 PM

  • Unarguably one of the best blogs on AoPS created by one of the most amazing people on AoPS :)

    by player01, Mar 24, 2022, 6:38 PM

  • Thank you for this wonderful resource, K-A! It's helped me a lot. Not many sites have asymptotic tutorials that make sense, or Google just understands "asymptote" wrong.

    by fuzimiao2013, Dec 12, 2021, 6:43 PM

  • wow you are a pro at asymptote great job klaus-anton!!!

    by HWenslawski, Oct 20, 2021, 5:24 PM

  • Amazing blog. You are so good at asymptote!

    by player01, Aug 27, 2021, 12:48 PM

  • ngl, Klaus-Anton is pr0 at LaTeX and asymptote

    by mathlearner2357, Mar 19, 2021, 9:44 AM

  • Thanks! This blog had a lot of asymptote functions that I needed for olympiad geometry diagrams.

    by eduD_looC, Mar 16, 2021, 12:28 AM

  • @player01 now 30k visits

    by ObjectZ, Feb 2, 2021, 2:14 PM

  • @pog now 29k visits :P

    by player01, Nov 11, 2020, 5:14 PM

  • 18 shouts and 26k visits?

    by pog, Sep 9, 2020, 3:48 PM

  • yeet
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    by ARay10, Sep 4, 2020, 4:21 PM

  • What software do you use to make asymptote diagrams?

    -πφ

    by piphi, Jun 18, 2020, 3:09 AM

  • dang this is an old blog

    by CoolCarsOnTheRun, Jun 7, 2020, 10:07 PM

  • Is it possible to export an asymptote drawing as an SVG?

    -piphi

    by piphi, May 12, 2020, 6:56 PM

  • Yah, I remember that...

    by sonone, May 1, 2020, 2:39 PM

  • Actually, the making pies thing is from AoPS challenge problems in PA2.

    by RedSox2, Apr 23, 2020, 4:53 PM

  • I like your blog. How did you learn so much?

    by sonone, Apr 3, 2020, 2:36 PM

  • nice blog!

    by matharcher, Mar 21, 2020, 2:10 AM

  • wow, this is awesome! Im subscribing

    by piphi, Feb 12, 2020, 8:28 PM

  • Yes sure it is!

    by mathboy282, Dec 21, 2019, 9:38 PM

  • I like this blog. It is very helpful.

    by Chishimotoji, Jan 23, 2019, 3:12 AM

  • Great blog!

    by WizardMath, Mar 9, 2018, 10:59 AM

  • Asymptote = good = probably better that I ever will be

    by coolmath34, Nov 23, 2017, 1:03 AM

  • Wow you are good at asy!

    by fuegocaliente, May 24, 2017, 9:20 PM

  • first shout of 2017!!

    by Mathisfun04, Mar 6, 2017, 3:00 PM

  • Nice asymptote!

    by Boomer, Apr 2, 2014, 4:22 PM

  • :blush: I wonder, I wonder.

    by Klaus-Anton, Jan 8, 2011, 6:19 PM

  • First shout!

    by El_Ectric, Jan 4, 2011, 9:14 PM

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