Difference between revisions of "2022 SSMO Speed Round Problems/Problem 7"
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==Problem== | ==Problem== | ||
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+ | 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== | ==Solution== | ||
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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
.