2025 SSMO Accuracy Round Problems/Problem 9

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 $k$ .

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2025 SSMO Accuracy Round Problems/Problem 9

Problem

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