I was told that when you defeat the puzzles you get a higher multiplier when you fight the real cogs. Is this true? No clue yet

It does seem there must be a purpose to the puzzles, though. We spent a lot of time in there last night figuring them out (rather - watching PTT figure them out while we chatted and looked cute

) and I think we actually did ace some of them...others we weren't quite sure how we did it.