Partition sequences of coin flips under the equivalence relation ~, where a~b if and only if the sequences differ in an even number of positions. For any equivalence class A, let A' be the equivalence class obtained by reversing the first flip in every member of A. For each pair {A,A'} of equivalence classes, choose one member of the pair and call that a "selected equivalence class". Then assign ON to all and only the sequences in a selected equivalence class.
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