Difference between revisions of "2022 SSMO Speed Round Problems/Problem 7"
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| + | ==Problem== | ||
| + | Let <math>A_1=(1, 0)</math>. Define <math>A_{n+1}</math> as the image of <math>A_n</math> under a rotation of either <math>45^{\circ}</math>, <math>90^{\circ}</math>, or <math>135^{\circ}</math> clockwise about the origin, with each choice having a <math>\frac{1}{3}</math> chance of being selected. Find the expected value of the smallest positive integer <math>n>1</math> such that <math>A_n</math> coincides with <math>A_1</math>. | ||
| + | |||
| + | ==Solution== | ||
Latest revision as of 19:14, 2 May 2025
Problem
Let 
. Define 
as the image of 
under a rotation of either 
, 
, or 
clockwise about the origin, with each choice having a 
chance of being selected. Find the expected value of the smallest positive integer 
such that coincides with 
.
