Difference between revisions of "2023 SSMO Relay Round 4 Problems/Problem 2"
(Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = \left\lfloor\sqrt{N}\right\rfloor.</math> Suppose that <math>N</math> points are chosen on the sides of a triangle with ar...") |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | Let <math>T=</math> | + | Let <math>T=TNYWR</math>. Let <math>n = \left\lfloor\sqrt{N}\right\rfloor.</math> Suppose that <math>N</math> points are chosen on the sides of a triangle with area 1 such that there is at least one point on each side. Let <math>m</math> be the area of the polygon formed by connecting the <math>N</math> points in counterclockwise order. Find the expected value of <math>\frac{30}{1-m}</math> |
(Note that <math>\left\{x\right\} = x - \lfloor x \rfloor</math>) | (Note that <math>\left\{x\right\} = x - \lfloor x \rfloor</math>) | ||
==Solution== | ==Solution== | ||
Latest revision as of 19:19, 2 May 2025
Problem
Let 
. Let 
Suppose that 
points are chosen on the sides of a triangle with area 1 such that there is at least one point on each side. Let 
be the area of the polygon formed by connecting the points in counterclockwise order. Find the expected value of 
(Note that 
)
