Sam Loyd was a wacky guy. His legacy of puzzles is well worth digging through. (I'd stay away from the 15/14 puzzle though.)
A sprinkling of his puzzles were chess-related, and plenty of them stand up well in the greater lexicon of chess puzzles. For example, his "Organ Pipes" mate-in-two problem is quite well known:
White to move and mate in two (Sam Loyd, 1859)
(If you haven't seen it before, go ahead and try it out. It's a cute little interference problem.)
OK, now we get to it.
From a technical point of view, there's a slight flaw here. Ideally, in a chess problem Black has very many options, and White has only a single path to victory in all variations.
This is not the case here. If the Bishop on f8 wanders away (1. ... Bg7, 1. ... Bh6) or is blocked by the Rook on e8 (1. ... Re7) then White has two mates: 2. Qb6# or 2. Qxb4#.
|1. Qa5||1. ... Bb7||2. Nf5#|
|1. ... Bd7||2. Qd5#|
|1. ... Be6||2. Qe5#|
|1. ... Bf5||2. Nxf5#|
|1. ... Rd7||2. Nf5#|
|1. ... Rd6||2. Qxb4#|
|1. ... Rd5||2. Qxd5#|
|1. ... Re7||2. Qb6# or 2. Qxb4#|
|1. ... Rd6||2. Nf5#|
|1. ... Re5||2. Qxe5#|
|1. ... Bc5||2. Qa1#|
|1. ... Bd6||2. Qd5#|
|1. ... Be7||2. Qe5#|
|1. ... Bg7||2. Qb6# or 2. Qxb4#|
|1. ... Bh6||2. Qb6# or 2. Qxb4#|
Luckily, the problem can be easily "fixed" - add a black pawn on a7:
White to move and mate in two
(Sam Loyd, 1859; version by Matthew van Eerde, 2008)
This covers the b6 square. Now the only mate is to take on b4.
Beauty is a tricky beast though. This is now a more "technically correct" problem, but the position is no longer quite as "natural"-looking. (I quote "natural" because I've seen plenty of ugly over-the-board positions.) The pawn on a6 must have come from b7, and the pawn on b4 must have come from c7 (or perhaps from further away.)
I'm not sure which version I prefer, but it's nice that the flaw is not serious.