To clear a puzzle(s) to play again or to improve your badge statistics, scroll to the bottom of the home screen and look for the "Solved >" section header.
Tap on the header and you'll see a long vertically scrolling list to review.
Next tap Select at the top and you can choose one, several, or select all/de-select.
If you are using an iPhone/iPad, the list also uses standard Apple select gestures — so you can use two fingers to drag down the list and it will select as you drag. This is great for clearing, say, the last 10 puzzles.
At the top, it will tell you how many puzzles you have selected, and that's what will be cleared when you tap the Clear button.
Once your done, you can scroll back up and the section counts will have increased to reflect the newly cleared puzzles.