2006 USAMO Problems/Problem 5

Problem

(Zoran Sunik) A mathematical frog jumps along the number line. The frog starts at 1, and jumps according to the following rule: if the frog is at integer $n$ , then it can jump either to $n+1$ or to $n+2^{m_n+1}$ where $2^{m_n}$ is the largest power of 2 that is a factor of $n . Show that if$ k\ge 2 $is a positive integer and$ i $is a nonnegative integer, then the minimum number of jumps needed to reach$ 2^i k $is greater than the minimum number of jumps needed to reach$ 2^i$.

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2006 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6
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2006 USAMO Problems/Problem 5

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