A failed puzzle is one that you don't successfully solve within 24 hours. As far as requesting a clue is concerned, I believe that if you request a clue, the puzzle is considered to be unsolved. However, I've never requested one, so I'm not positive about this. If you submit an incorrectly solved puzzle, you just click on the return to puzzle icon to solve it correctly, often by clearing the grid and starting over. If you try several times and just can't solve it correctly, you can always do something else and come back to it with fresh eyes within 24 hours by viewing recent puzzles and clicking the retry button. It then comes back up for you to solve. However, doing so will inflate your average time since the timer runs from the moment you click the Start the Puzzle icon. I've done many puzzles and never found one that didn't have a correct, logical solution. I've believed that a puzzle didn't have one. However, upon returning to it, I've always found that it did have one.