You can't do it in 2 or 3 weeks if you want to have a good quality.
I disagree: You can create a good quality game in just a few weeks if you are determined. It also helps if you have external sources to provide media and levels.
Most of the best puzzle games tend not to require lots of assets - graphics, music or sfx. They just need a compelling puzzle mechanic. Look at Tetris, Puzzle Bobble (Bust-A-Move), Columns etc.
The puzzles themselves (for level based puzzlers) are what takes the most time to create and if you make them randomly or procedurally or create a puzzle generator, then these can be done in no time.
People who know me, know that puzzles are what I do best - B'lox!, Guru Logic Champs, SuQo, Ken2X, MinedOut!, CodeCrack, Frootopia, Hallowian and AquaVenture are just some of the puzzle games I've created/coded.
Coming up with a good mechanic is the hardest thing in creating a puzzle game- if MrPlow has already done that (but not coded it), then he's more than 50% there already.