When I was younger, I made a lot of jigsaw puzzles, and I still enjoy the occasional diversion once or twice a year. My first memory of making a puzzle was a 100-piece puzzle I used to make all the time as a little kid (probably 4-5 years old). Over time the puzzles grew more complex, and I eventually worked my way up to finishing 1,000-piece puzzles in a week or less. I made puzzles hardcore. I still consider looking at the picture on the box to be cheating after the puzzle has been started.
Most of the puzzles I made were pretty basic, with the only issue in putting it together being the occasional missing piece. They are not very memorable. Other puzzles, especially later on, were not typical puzzles, including puzzles where each piece had at least one straight edge; puzzles with pieces inside other pieces; a double sided puzzle with the same picture on each side, rotated 90°; and one that was likely my family's attempt to prevent me from ever again only asking for puzzles for my birthday or Christmas: a 750-piece puzzle with no edges, 5 extra pieces, and a picture (not even as shown on the box) that was entirely golf balls, golf tees, and grass. That took me at least 1-1/2 years to finish, and, though it did have the effect of greatly lessening my desire to make puzzles, it was far more satisfying to finish than most puzzles are. It is also never coming apart, beyond the four pieces it is in to fit back in the box.
Composing can be a lot like making a puzzle. On rare occasions you are able to see what the puzzle is supposed to look like as you work; this is generally more true of transcribing and arranging. Other times, you get a brief glimpse of the picture before you start, but your idea of what it was changes as you are putting it together. Most often, you are building a puzzle without having seen the picture on the front of the box. There are often, in composing, missing pieces that need to be created to connect two sections together, pieces that don't fit quite right and need to be shaped for a perfect fit, small pieces that need to be inserted in to larger pieces of the puzzle, and extra pieces that do not actually fit anywhere and should be removed.
Some compositions are like basic puzzles. These can include things like lead sheets (typically melody and chords, with lyrics if applicable) and many typical pop songs. They are usually quickly created, but only partially satisfying. While they can be enjoyable for a composer, performer, and audience, they can often be either easily remade in a better form or forgotten entirely without much sense of loss for the first composition of the piece. Then there are compositions that are more like a complex puzzle. These can include things like orchestral or chamber ensemble pieces, among other things. They are usually time-consuming to compose, and are very satisfying to finish. Once completed, there is generally no need to change anything beyond perhaps minor editing, so the work is left as is, and any future arrangements of it are generally lesser versions.
Some puzzles look pretty, but there is little to challenge the builder with, while others obviously had a great amount of thought put into both appearance and construction. The same goes for music: some music sounds great, but is fairly simple in it's composition (which can be perfectly fine); other music is both pleasing to listen to and has a great amount of depth put into it by the composer.
Composing is the ultimate jigsaw puzzle.