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Omni-MATH / Ashwin the frog is traveling on the xy-plane in a series of 2²⁰¹⁷−1 steps, starting at the origin. At the n^(th ) step, if n is odd, then Ashwin jumps one unit to the right. If n i…

Problem

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problem

Ashwin the frog is traveling on the xyx y-plane in a series of 22017−12^{2017}-1 steps, starting at the origin. At the nth n^{\text {th }} step, if nn is odd, then Ashwin jumps one unit to the right. If nn is even, then Ashwin jumps mm units up, where mm is the greatest integer such that 2m2^{m} divides nn. If Ashwin begins at the origin, what is the area of the polygon bounded by Ashwin's path, the line x=22016x=2^{2016}, and the xx-axis?
Plain-text mathematical notation (without MathML)
Ashwin the frog is traveling on the xy-plane in a series of 2²⁰¹⁷−1 steps, starting at the origin. At the n^(th ) step, if n is odd, then Ashwin jumps one unit to the right. If n is even, then Ashwin jumps m units up, where m is the greatest integer such that 2^(m) divides n. If Ashwin begins at the origin, what is the area of the polygon bounded by Ashwin's path, the line x=2²⁰¹⁶, and the x-axis?
Original LaTeX notation
Ashwin the frog is traveling on the $x y$-plane in a series of $2^{2017}-1$ steps, starting at the origin. At the $n^{\text {th }}$ step, if $n$ is odd, then Ashwin jumps one unit to the right. If $n$ is even, then Ashwin jumps $m$ units up, where $m$ is the greatest integer such that $2^{m}$ divides $n$. If Ashwin begins at the origin, what is the area of the polygon bounded by Ashwin's path, the line $x=2^{2016}$, and the $x$-axis?

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Source and history

task_id
317f442e-ad54-55a5-a33b-d7a7484362d6
task_key
test--317f442e-ad54-55a5-a33b-d7a7484362d6
task_revision_id
1
config / split
/ test

Official source

initial import