Like, I suspect, most practical chess players, I prefer problems to be fairly clear but surprising: a quality that Loyd, who composed very much for the bafflement of his solvers rather than out of abstract aesthetic considerations, brought to the genre par excellence. He improved on his contemporaries' ideas and contributed some of his own; but the emphasis was always on his supremely light touch - at that time unfashionable, but for me delightful.
As a relative amateur in this field, I hope my crude comments are not too irksome for the cognoscenti. I guess it must be equivalent to someone, enthusiastic but under-informed, waxing lyrical about the wonderfully pellucid games of Siegbert Tarrasch as compared to the murky efforts of the young popinjays today; or, to be more controversial, to those (himself among them) who still consider Fischer to be world champion. Here, anyway, is one of Loyd's many deceptively simple-looking settings:
Mate in three
Sam Loyd 1869
This problem was published in the Leipziger Illustrierte Zeitung in 1869. White's task is to arrange to aim the queen at h7 while simultaneously attacking the black bishop. The bishop has five more squares available on the long black diagonal. But it turns out that there is one square from which she can always achieve this.
The solution is:
putting Black into zugzwang. The g pawn is prevented from moving in view of 2 Qxa1 mate, which leaves:
a) one pretty if somewhat unthematic variation: 1... g3 2 Ng6+ hxg6 3 Qh3#; and three thematic:
b) 1... Bb2, 1... h6 or 1... h5 2 Qb1!
c) 1... Bc3 or 1... Bd4 2 Qd3!
d) 1... Be5 or 1... Bf6 2 Qf5!