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.
Edit: no using add subtract multiply or divide more than once.
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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.)
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
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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
4TH POST LETS GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
This post has been edited 1 time. Last edited by PTV, Today at 2:25 AM
Reason: I mistyped something
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.
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
, the continent is divided into
regions, as shown. Dragon island, far in the northeast, has just birthed
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
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
region. As you ask your scouts what they saw, you realize in horror that they said they scouted
fire,
ice,
lightning, and
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?
4. In the land of









You have 10 minutes. (not really) Which 2 regions should you bisect to save the continent?
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
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 
Sorry if this has a lot of brainrot lol. I thought of this while listening to brainrotted kids as a summer volunteer

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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