Small Engines (Lawn Mowers, etc.): Craftsman Riding Mower, craftsman riding mower, internal passages

Question
about 10 year old craftsman riding mower (1030).  I bought this used and I'm not sure how old it is.  The first time I used it it worked fine for about 15  minutes. Then it began sputtering and backfiring and finally stalled.  I couldn't get it to run consistently after that.  I tried again the next day and it ran ok for another 20 minutes or so so I was able to finish the lawn.  A few weeks later (today) the same scenario played out although I haven't tried again.  I triedd adjusting the the carb settings(Power adjusting screw and idle valve screw) as described by the manual, but no luck.  Now I can't get it to start. Any suggestions?

Answer
If you get no response by adjusting the mixture screw, there is a blockage inside the carb.  It is likely that debris has contaminated the fuel system (and perhaps your gas can too).  Thoroughly clean the carb, including pushing a piece of tag wire through all of the internal passages, replace the fuel filter and inspect the tank for debris or sediment.  Hope this helps.