George Jelliss, in Variant Chess, issue 22 (Winter 1996/1997), wrote a very nice article about Cylinder Chess. I took the liberty of taking two of the chess problems from that article, and publishing them here. The article features a description of Byzantine chess, four more cylinder chess problems, and many progressive cylinder chess games from AISE competitions.
The following problem is from A. W. Mongredien, Bulletin de la FFE, No. 19, 1926.
The rules are: the left and right side of the board are considered to be connected, and pieces are allowed to move across it, rooks, bishops, and queens following the same lines. Thus, e.g., a queen can go from b4 to g1 (via a3 and h2).
King a3; Rook h4, h6.
King b5; Pawn c5, c6.
White to move and mate in two. Cylinder Chess.
Try also to solve another Cylinder Chess problem.