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2025 SSMO Accuracy Round Problems/Problem 9

Revision as of 11:26, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== For a positive integer <math>n,</math> let <math>r(n)</math> denote the value of the binary number obtained by reading the binary representation of <math>n</math>...")
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Problem

For a positive integer $n,$ let $r(n)$ denote the value of the binary number obtained by reading the binary representation of $n$ from right to left. For example, $r(6) = r(110_2) = 011_2 = 3$. If $k$ is the smallest positive integer such that the equation $n+r(n)=2k$ has at least ten positive integer solutions $n,$ find $k$.

Solution

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