Some reasons why two dimensions aren't popular
I see two weaknesses of the small puzzles.
First, there is a strong temptation to make puzzles about people. That means names are one common dimension. If we restrict to two dimensions, then the puzzles are all of the form "match the people on this list with one of their attributes from this other list." That quickly feels repetitive.
I'm open to the idea that this is just my own weakness as a puzzle writer, maybe exacerbated by the fact that I've just started trying to write these. If so, then I should be able to create more interesting contexts over time. Puzzle 3 is in that spirit.
Second, structurally, 2 dimensional puzzles are missing some important and difficult inference rules. Let's use the terms (names and instruments) from my Puzzle 1 and add another dimension where the kids like different sports (football, tennis, volleyball, and biking). Taken from this paper, the key inference rules are:
- Related by elimination. For example, if we know that Aaron doesn't play violin, trumpet, or drums, then he must play piano.
- Not related by exclusion. For example, if the violin is played by Carly, the it isn't played by Aaron, Benjamin, or Diana
- Related by transitivity: No example from Puzzle 1. Using the extra dimension, if Benjamin plays violin and the violin player likes biking, then we can conclude Benjamin likes biking.
- Not related by transitivity: Again, our basic puzzles can't illustrate this. Illustrating with the extra dimensions, say Carly doesn't play piano and the piano player likes tennis, then Carly doesn't like tennis.
Empirically, the transitivity rules make puzzles much harder, partly because the grids make the other two rules visually clear.
Anyway, I'll test these out with the kids and report back.