That was very enjoyable. I only played two levels but on the black and white puzzle the timer never started (the second one I did). I wish there was a way to stop the music Being disjointed was very distracting early on. And I didn't like that clicking instantly gave you the next piece if you only clicked empty space. Making it kind of like Mastermind (the idea of the bar) was a great idea.
When putting together the catapult you can put the pieces on and then trade them as well. If you don't do anything between putting them on the catapult and trading.
 "Click Champion"){kind=icon}
 "The Armony Jigsaw"){kind=icon}
 "Dibbles: For The Greater Good"){kind=icon}
 "Another Small Favor"){kind=icon}
 "Ragdoll Cannon Four"){kind=icon}