You could also sort of compose a new piece. That might be fun...
Like aleatoric music.
Aleatoric means random and is derived from the Latin for dice. The idea here of course is that the puzzle pieces would just be just stuck together at random from a mixed pile. Chances are this isn't actually possible because the edges are likely to be cut so that the shape of every piece is different and they will only fit together one way. Though it would be pretty cool if the pieces were designed to be of identical shape and contained one bar or so of music each.
But did you know that Mozart wrote some literally
aleatoric music? This was posthumously published in 1773 by Hummel and republished in 1798 by Simrock. I have a 1976 facsimile reprint of this 2nd edition. It is a recipe for "composing" simple waltzes without needing to have the slightest knowledge of harmony or composition and is almost like a game. It requires two dice.
The aim is to generate an 8-bar minuet-like piece plus an 8-bar trio section. What Mozart did was to write 11 different versions of each of the 16 bars required, each version of one bar is a good fit with all versions of its neighbours. So he wrote 176 bars and gave each bar an ID number. Then he compiled two tables, one for the menuet and one for the trio, labelling the columns A to H in each case (to represent the 8 bars of the section). The rows were numbered 2 to 12, representing the 11 possible sums you can get by throwing two dice.
So you throw the dice. Say you get 3 and 5, which makes 8. So you look up row 8 and column A to find an ID number. So for the first bar of your "customised" waltz, you just copy out the bar which has that number. Repeat the process for each of the other 15 bars and there's your finished product.
It is easy to see that the number of different waltzes that you can "compose" this way is huge. There are over 214 million different minuets and the same number of trios, hence almost 46 quadrillion different complete pieces, or there would be if each bar's 11 versions really were all different, which is not quite the case. But there is still a plenty of variety.