# Difference between revisions of "G285 2021 MC10B"

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==Problem 5== | ==Problem 5== | ||

+ | A principal is pushing out an emergency COVID-19 alert to his school of <math>40</math> teachers and <math>500</math> students. Suppose the announcement is first approved by his <math>5</math> aides. Then, each of the aides share the announcement to <math>n</math> teachers and <math>t</math> students, where <math>n,t \in \mathbb{Z}</math> and for every aide <math>n \neq t</math>. Moreover, <math>n+t = (u+1)^2</math>, where <math>u</math> is the round number ( for the first notice it is round 1, then round 2....) After every round <math>u</math>, some <math>k</math> teachers in the previous round share the announcement to a new group of <math>n</math> teachers and <math>t</math> students, where <math>k=(u+1)^2</math>. How many rounds will it take until the entire school is informed? Assume that after all teachers are informed, <math>n=0</math>, but <math>t</math> still grows as if <math>n \neq 0</math>. | ||

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+ | <math>\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math> |

## Revision as of 18:47, 14 May 2021

## Problem 1

Find

## Problem 2

If , and , and , what is ?

## Problem 3

A convex hexagon of length is inscribed in a circle of radius , where . If , and , find the area of the hexagon.

## Problem 4

Find the smallest such that:

## Problem 5

A principal is pushing out an emergency COVID-19 alert to his school of teachers and students. Suppose the announcement is first approved by his aides. Then, each of the aides share the announcement to teachers and students, where and for every aide . Moreover, , where is the round number ( for the first notice it is round 1, then round 2....) After every round , some teachers in the previous round share the announcement to a new group of teachers and students, where . How many rounds will it take until the entire school is informed? Assume that after all teachers are informed, , but still grows as if .