Play Dev 2.0 for 600 np in under 1 minute. You just click any option, you don't actually have to read the answers. Just click an answer for every question and you'll have 200 NP in just seconds.
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From the Bazaar, you can get to the Survey Shack or just go to here:
http://www.neopets.com/sponsors/surveyshack/index.phtml?sc9ejf2=73507 and get 3250-4000 neopoints a day.
Click Majority Rules.
Play Majority Rules for 3000 NP per day....
http://www.pinkpt.com/forum/viewtopic.php?t=26054 keep this open while you play Majority Rules, to get the right answers. If you are a member of SurveySmash (free) you get double points, and you get two NP per point scored in the game, meaning that you only have to get a score of 250 to get 1000 np per play. Simple enough if you use that thread with all the answers!
Click on Loyalty Program
If you are a surveysmash member, you just have to move your mouse around on the screen until you see a red "NP". Click on it and that's 250 free NP.
Click on Super Daily Survey.
Just click the button to make the ball drop. You can drop it up to 3 times. Usually if I get 200 I just end game and take the points, rather than risk losing part of it. However, you can drop the ball and see where it is going to land, and if it goes into a "lose NP" box, you can end game before the change is applied.
This wins you from 20-400 np per play, depending on your luck. It's free np though, no skill required, so play away.
So there is 4000 np per day in about 10 minutes.
NOT playing Dev2.0 and Majority Rules every day is probably one of the silliest oversights you can make on Neopets. The time investment is very small, but the payoff is very high, and it's pure profit - you don't have to pay any NP to get NP here.
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Ultimate Bullseye has one of the highest payouts of all the games - 8 np for every 1 point scored. That means even if you are pretty bad at the game like I am, and only get a score of about 15-20, then you'll still get 120-160 NP per play. It only takes a minute to play, so you've got about 450 NP in 2-3 minutes.
So, those three things alone give you nearly 5000 NP in under 20 minutes, every day! not bad eh?
Usuki Frenzy is also a fast-play game that gives you points even when you're bad at it. It can't possibly take more than 2 minutes per play (because there is a timer) and one time I tried getting EVERY SINGLE WRONG SET on purpose, and having to put them all back (something you can avoid doing if you don't rush) and ended with only 12 seconds to spare, and I still got 82 points, which was 123 neopoints! So that's another 400 np or even more, in just 6 minutes or less.
I want to emphasize that you don't have to be good at games to get NP, but you should try every single game at some point to figure out whether there are any you ARE good at. That way, you know what to focus on. Plus, you'll be closer to getting the gamer avatar that way