The clock app in cyanogen has a timer and stopwatch n stuff.
As far as the alarm goes, I just use the stock one. You can make multiple ones and select the days it repeats and whatever, it just doesn't have the puzzles you are hinting at.
Android 4.2's Clock app does Alarms, countdown and stopwatch... so that's what I use.
Back when I was on Android, my go-to Alarm app was Gentle Alarm. It was never aesthetically pleasing, but it worked well. Not sure if it's still good though.
Alarm Clock Xtreme
I use alarm clock plus. It's a paid app but it gives you al the things you stated you want to do with your alarms except the puzzle solving part. I just put three or four alarms on. There is a free version too with ads.
I use a combo of the free Alarm Clock Plus (Doesn't have puzzles but has math problems of varying, selectable difficulty) and a Holo-themed 'Kitchen Timer' (pic below) that I'm pretty sure I found on XDA, since there is no market version except the vanilla one.
Given that, when I finally get to 4.2 I'll probably just use the stock app
Thanks for the tips. I'm going with Alarm Clock Plus now which seems to do what I want. Math is fine for a puzzle. I like that the alarm stops for a few seconds while you type your answer, SPB just kept going untill you got it right.
I'm also trying the Kitchen Timer (the one in the android store, not as pretty but looks to have the same elements as the screenshot). It doesn't seem to remember my last couple of alarms though at a glance, but I've not played around much with it yet.
I just used the clock app after getting the update to 4.2 on my old Nexus. Prior to that I used a math-based alarm app that made you answer questions because it worked really well for getting me up earlier than I would otherwise.