First, take as much water out of your toilet bowl as possible, and fill up a plastic bottle with warm water. After donning a pair of rubber gloves (or large plastic bags, in a pinch), plug the top of the bottle with your thumb, and place the bottle and your thumb at the mouth of the pipe. Then, remove your thumb and squeeze the bottle to propel the water, and hopefully the clogged mass, through the pipe.
I see so many chances of a nasty accident.
There's another trick that can work or be disastrous:
Slightly wet the border of the toilet, then put a closed plastic litter bag over it, to form a kind of seal. Put some unfolded newspaper over it to create a thick layer. Put down the seat and seat on it. Press the button and pray. Hopefully, your "seal" will hold the air inside, increasing the internal pressure and forcing the clog down. If your seal fails, you'll have shitty water all over the place.
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