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Difference between revisions of "2023 SSMO Relay Round 5 Problems/Problem 3"

(Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math>...")
 
 
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==Problem==
 
==Problem==
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Let <math>T=</math> TNYWR. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math> is divided by <math>100,</math> where <math>a</math> and <math>b</math> distinct members from the set <math>\{1,2,\dots,N\}.</math>
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Let <math>T=TNYWR</math>. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math> is divided by <math>100,</math> where <math>a</math> and <math>b</math> distinct members from the set <math>\{1,2,\dots,N\}.</math>
  
 
==Solution==
 
==Solution==

Latest revision as of 19:20, 2 May 2025

Problem

Let $T=TNYWR$. Suppose that $x^2+y^2 = N.$ Find the remainder when the expected value of the square of the maximum value $ax+by$ is divided by $100,$ where $a$ and $b$ distinct members from the set $\{1,2,\dots,N\}.$

Solution

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