3 problems

Double-sequencing conjecture. All groups of order at least $4$ are doubly sequenceable, doubly R-sequenceable, doubly harmonious, and doubly R-harmonious.

Bailey's conjecture. All finite groups, except the elementary $2$-groups of order at least $4$, are $2$-sequenceable.

Anderson's conjecture. All binary groups except the quaternion group $Q_8$ are symmetric sequenceable.