Interactive fiction author Emily Short offers a thoughtful analysis of the function of designing puzzles that permit the player to come up with original solutions. She refers to her game Metamorphoses, which includes a complex physical world model that includes such concepts as size, shape, weight, etc.  For instance, you can beat down a door by enlarging a needle so that it is the size of a battering ram, and you can turn your simple clothing into a suit of armor by converting the material from natural fibers to metal.  I wish I had the time today to give her thoughts the attention they deserve…

Metamorphoses includes several in-game processes (resizing objects, breaking objects, changing the material substances of objects, piercing objects with a needle), and it’s possible to string these together — change an item to glass and then break it, say, or change an item to something that isn’t too hard, then pierce it, then resize it so that the hole is large, then change the item into a heavier substance… But I did anticipate most of these sequences, in part because there weren’t that many problems available to be solved. Emergent solutions tend to happen more often when there are a large number of puzzles, so that the world model developed to account for problem A can also be leveraged, unexpectedly, against problem B. So such games also probably need to be of a reasonable size.

So I hypothesize that a game allowing emergent solutions needs all of the following:

• attributes common to most game objects that affect interaction
• processes, effective on many game items, that allow the player to change attributes (or produce an item with new attributes out of an old item, as in the case of breaking the tail off the rat)
• a selection of processes that can be used in combination (freeze rat then smash it); one way to think about this at the design phase might be to draw a chart of attributes and processes, showing which processes convert which attributes into which others; the more long chains are possible, the more complex the plans the player can execute
• sufficient number of puzzles that the solution space becomes too large for the author to anticipate at the design phase 

Once we have all those features, though, we run into some other serious design problems.