Quote: "Price of Persia Sands of Time had a lot of puzzling--- jumping, climbing, swinging, etc. Plus it should be fairly cheap now and will run in backwards compatibility mode on the 360 "
I would also reccomend Prince of Persia, a lot of the gameplay involves a balance between fighting and exploring (Lots of jumps and running along walls etc.) and there's a bit of puzzle solving too such as pulling switches and levers and working out where to go next, I know that on the ps2 you can buy all three games (Sands of time, Warrior within and Two thrones) in a grouped trilogy. It's called "Prince of Persia Trilogy" (surprising eh?). I got it for £14 (Roughly $30) so thats three games, each costing £4.67... that's a mighty good deal if you ask me
I'm not sure about if this trilogy is on the other consoles you mentioned...