The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of and is closest to which integer?

The one-way routes connecting towns , , , , , and are shown in the figure below (not drawn to scale).The distances in kilometers along each route are marked. Traveling along these routes, what is the shortest distance from A to Z in kilometers?

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A box contains chips, numbered , , , , and . Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds . What is the probability that draws are required?

In convex cyclic quadrilateral , we know that lines and intersect at , lines and intersect at , and lines and intersect at . Suppose that the circumcircle of intersects line at and , and the circumcircle of intersects line at and , where and are collinear in that order. Prove that if lines and intersect at , then .

Proposed by Kada Williams

Please write down your goal/goals for competitions here for 2025-2026.

(trying this again in a different thread now that it's later)

I've been accepted into Camp Conway, which is a part of National Math Camps, a organization of Math Camps that currently includes two: Camp Conway and Camp Sierpinski. Camp Conway is located at Harvey Mudd in California and happens during the first half of summer, while Camp Sierpinski is in North Carolina's research triangle and happens during the second half. Each of them has two two-week long sessions that accept 30 people (it's very focused on social connection), which means 120 people will be accepted to the program in total.

Given how much of the math community is on aops, I think there's a decent chance one of the 120 people might see this thread. So - has anyone here been accepted into Camp Conway or Camp Sierpinski? If so, which session are you going during, and what are you looking forward to?

I'll be attending during the second session of Conway in the first few weeks of July - I'm looking forward to the Topics Classes as a lot of them sound pretty fun.

Anyone already got results for HCSSiM? Are there any point in sending additional work if I applied on March 19?

[center] :trampoline: :first: Stanford Math Tournament :first: :trampoline: [/center]

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We are excited to announce that registration is now open for Stanford Math Tournament (SMT) 2025!

This year, we will welcome 800 competitors from across the nation to participate in person on Stanford’s campus. The tournament will be held April 11-12, 2025, and registration is open to all high-school students from the United States. This year, we are extending registration to high school teams (strongly preferred), established local mathematical organizations, and individuals; please refer to our website for specific policies. Whether you’re an experienced math wizard, a puzzle hunt enthusiast, or someone looking to meet new friends, SMT has something to offer everyone!

Register here today! We’ll be accepting applications until March 2, 2025.

For those unable to travel, in middle school, or not from the United States, we encourage you to instead register for SMT 2025 Online, which will be held on April 13, 2025. Registration for SMT 2025 Online will open mid-February.

For more information visit our website! Please email us at stanford.math.tournament@gmail.com with any questions or reply to this thread below. We can’t wait to meet you all in April!

If I am aiming for AIME, then JMO afterwards, is Alcumus adequate, or I still need to do the problems on AoPS books?

I got AMC 23 this year, and never took amc 10 before. If I master the alcumus of intermediate algebra (making all of the bars blue). How likely I can qualify for AIME 2026?

Just wanted to ask

hi guys, i'm about to be an incoming freshman, does anyone have recommendations for classes to take next year and camps this summer? i am sure that i can aime qual but not jmo qual yet. ty