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Difference between revisions of "AIME 2020(MOCK) Problems"

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==Problem 3==
 
==Problem 3==
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How many <math>15</math> digit base <math>5</math> positive integers consist of exactly <math>2</math> pairs of consecutive <math>0</math>s but no <math>4</math> consecutive <math>3</math>s?

Revision as of 12:12, 11 June 2020

Problem 1

Let $N$ be $112123123412345... (1000 digits)$. What is the remainder when $N$ is divided by $21$?


Problem 2

Let $K$ be a set of polynomials $P(x)$ with integral coefficients such that the roots of $P(x)$ are $cos \frac{\pi}{7}$, $cos \frac{\pi}{11}$, and $cos \frac{\pi}{17}$. What is the least possible sum of the coefficients of $P(x)$?


Problem 3

How many $15$ digit base $5$ positive integers consist of exactly $2$ pairs of consecutive $0$s but no $4$ consecutive $3$s?

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