Puzzle 4

Find a permutation p of { 1, 2, ..., 567 } such that, for each i in the domain, i + p(i) is a power of 2.

There's nothing special about 567. There's a solution for all positive integers.

Source: Zhi-Wei Sun, On Permutations of {1,...,n} and related topics, J. Algebraic Combinatorics 54 (2021) 893-912; via Stan Wagon's Problem of the Week no. 1362.

An answer to puzzle 4.

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