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Which programming language(s) would you guys recommend for coding puzzle programs like the ones found on this website? (And btw, I highly recommend the puzzle collection there.) I'm just looking for a language that can handle simple 2D graphics and mouse input with relative ease, and I don't particularly care if the result is web-based or not.

As for my own knowledge, I'm only familiar with the basics of C.

Actionscript 3 (Flash) (expensive), Lua w/ Love2d, or Python w/ PyGame.

Python probably has the lowest barrier to entry because Flash costs money and Lua lacks guides for newbie programmers (and I can't teach).

Those look like something Game Maker would handle well. Not that I've ever used Game Maker, but maybe someone else can back it up. I know it has a GUI toolset, so I'm sure it has the lowest barrier of entry out of any choices you have. Although it only outputs .exe files, so it won't work on Mac if that bothers you.

This is me not backing up Game Maker. Maybe I'm not too inventive with what's there, but it's really limited in what it offers.