Alcumus vs books
by UnbeatableJJ, Apr 23, 2025, 12:58 PM
This post has been edited 1 time. Last edited by UnbeatableJJ, Yesterday at 2:32 AM
Stanford Math Tournament (SMT) 2025
by stanford-math-tournament, Feb 1, 2025, 3:16 AM
Stanford Math Tournament
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!
Graph Theory?!?!??!?2.?!!>2r
by pog, Oct 11, 2024, 3:00 PM
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?
![[asy]
/* AMC8 P14 2024, by NUMANA: BUI VAN HIEU */
import graph;
unitsize(2cm);
real r=0.25;
// Define the nodes and their positions
pair[] nodes = { (0,0), (2,0), (1,1), (3,1), (4,0), (6,0) };
string[] labels = { "A", "M", "X", "Y", "C", "Z" };
// Draw the nodes as circles with labels
for(int i = 0; i < nodes.length; ++i) {
draw(circle(nodes[i], r));
label("$" + labels[i] + "$", nodes[i]);
}
// Define the edges with their node indices and labels
int[][] edges = { {0, 1}, {0, 2}, {2, 1}, {2, 3}, {1, 3}, {1, 4}, {3, 4}, {4, 5}, {3, 5} };
string[] edgeLabels = { "8", "5", "2", "10", "6", "14", "5", "10", "17" };
pair[] edgeLabelsPos = { S, SE, SW, S, SE, S, SW, S, NE};
// Draw the edges with labels
for (int i = 0; i < edges.length; ++i) {
pair start = nodes[edges[i][0]];
pair end = nodes[edges[i][1]];
draw(start + r*dir(end-start) -- end-r*dir(end-start), Arrow);
label("$" + edgeLabels[i] + "$", midpoint(start -- end), edgeLabelsPos[i]);
}
// Draw the curved edge with label
draw(nodes[1]+r * dir(-45)..controls (3, -0.75) and (5, -0.75)..nodes[5]+r * dir(-135), Arrow);
label("$25$", midpoint(nodes[1]..controls (3, -0.75) and (5, -0.75)..nodes[5]), 2S);
[/asy]](//latex.artofproblemsolving.com/9/3/7/937e770e18903819330e195c68a57256dec0b6f0.png)
, 
, 
, 
, 
, 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?![[asy]
/* AMC8 P14 2024, by NUMANA: BUI VAN HIEU */
import graph;
unitsize(2cm);
real r=0.25;
// Define the nodes and their positions
pair[] nodes = { (0,0), (2,0), (1,1), (3,1), (4,0), (6,0) };
string[] labels = { "A", "M", "X", "Y", "C", "Z" };
// Draw the nodes as circles with labels
for(int i = 0; i < nodes.length; ++i) {
draw(circle(nodes[i], r));
label("$" + labels[i] + "$", nodes[i]);
}
// Define the edges with their node indices and labels
int[][] edges = { {0, 1}, {0, 2}, {2, 1}, {2, 3}, {1, 3}, {1, 4}, {3, 4}, {4, 5}, {3, 5} };
string[] edgeLabels = { "8", "5", "2", "10", "6", "14", "5", "10", "17" };
pair[] edgeLabelsPos = { S, SE, SW, S, SE, S, SW, S, NE};
// Draw the edges with labels
for (int i = 0; i < edges.length; ++i) {
pair start = nodes[edges[i][0]];
pair end = nodes[edges[i][1]];
draw(start + r*dir(end-start) -- end-r*dir(end-start), Arrow);
label("$" + edgeLabels[i] + "$", midpoint(start -- end), edgeLabelsPos[i]);
}
// Draw the curved edge with label
draw(nodes[1]+r * dir(-45)..controls (3, -0.75) and (5, -0.75)..nodes[5]+r * dir(-135), Arrow);
label("$25$", midpoint(nodes[1]..controls (3, -0.75) and (5, -0.75)..nodes[5]), 2S);
[/asy]](http://latex.artofproblemsolving.com/9/3/7/937e770e18903819330e195c68a57256dec0b6f0.png)
Lots of Cyclic Quads
by Vfire, Apr 19, 2018, 11:00 PM
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
, 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
This post has been edited 2 times. Last edited by djmathman, Jun 22, 2020, 5:49 AM
A box contains 5 chips numbered 1, 2, 3, 4, 5
by CobbleHead, Feb 16, 2018, 6:06 PM
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?
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?
This post has been edited 3 times. Last edited by djmathman, Feb 17, 2018, 4:29 AM
May 2025
April 2025
March 2025