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MatPlus.Net Forum Promenade Cylinder twin challenge (no, v, h, both)

### Cylinder twin challenge (no, v, h, both)

I challenge readers to do a problem with at least FOUR twins, as follows:

a) Stipulation [St.]
b) St., vertical cylinder
c) St., horizontal cylinder
d) St., both cylinders

They obviously need to have different solutions.
Any stipulation would be fine, but "usual" ones (Mate, Selfmate, Helpmate, Stalemate, Helpstalemate, Helpselfstalemate, etc.) would be preferred. But of course if you find nothing else, "get knight b1 to d4 in 3 moves" or such will do.
Also, no fairy pieces is preferred, but if you need to use them, do so.

Does a problem like that already exist?

No prizes offered.

https://pdb.dieschwalbe.de/search.jsp?expression=k%3D%27vertik%27+and+k%3D%27horiz%27+and+k%3D%27torus%27
There are three such problems in PDB: h#2 and two ser-h#3.
May be more in WinChloe, of course

(3) Posted by Hauke Reddmann [Sunday, Aug 1, 2021 12:14]

I dimly remember that an "orthodox" #2 exists.

Millman and Volet, The Problemist, 1980
White: Kf8, Qb7, Sg1, Sh5
Black: Kh8, Sa3, Sd4
#1
a) Normal Board Qg7#
b) Vertical Cylinder Qa7#
c) Horizontal Cylinder Qh7#
d) Torus (Anchor Ring) Qa8#
e) Vertical Moebius Qa2#
f) Horizontal Moebius Qg8#

I found a #1:

(= 3+3 )

Die Schwalbe 1954
#1
b) Vertical cylinder
c) Horizontal cylinder
d) Torus board

And of course, why stop at regular cylinders?

(= 7+5 )

Stephen L. Millmann
Die Schwalbe 1981
#1
b) Vertical cylinder
c) Horizontal cylinder
d) Torus board
e) Vertical moebius
f) Horizontal moebius
g) Vertical cylinder, horizontal moebius
h) Horizontal cylinder, vertical moebius

I guess the 9th would be double moebius, aka projective plane.