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G285 2021 Fall Problem Set

Revision as of 13:56, 8 July 2021 by Geometry285 (talk | contribs) (Created page with "Welcome to the Fall Problem Set! There are <math>15</math> problems, <math>10</math> multiple-choice, and <math>5</math> free-response. ==Problem 1== Larry is playing a logi...")
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Welcome to the Fall Problem Set! There are $15$ problems, $10$ multiple-choice, and $5$ free-response.

Problem 1

Larry is playing a logic game. In this game, Larry counts $1,2,3,6, \cdots$, and removes the number $r+p$ for every $r$th move, skipping $r+jp$ for $j \neq 0 \mod 3$ and $j>0$, and then incrementing $p$ by one. If $(r,p)$ starts at $(1,3)$, what is $r+p$ when Larry counts his $100$th integer? Assume $\{r,p,j \} \in \mathbb{N}$

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