I have model 917.272751 tractor when I go to start after 1 week it will not turn over makes a attempt then stops replaced battery no change. Then noticed gas from exhaust to out plug cylinder full of fuel. Turned engine over with plug out blew out gas cleaned plug it started and ran fine stop and start for rest of day 1 week latter same thing could it be fuel solenoid?

Check your needle valve on the float bowl... thats your primary means to stop fuel once the proper float level is achieved.

I also hope you have been replacing that oil every week after it does this... because if the cylinder is filling with fuel... a lot more is diluting your oil in the crankcase as well. If you haven't you are destroying the bearings and will soon need a new engine.