There are two (general) kinds of drain cleaner. The ingredients will say
either hydroxide, or acid.
Hydroxides are used to remove grease, hair, and biological materials. Acids
will remove calcium scale. I'd suggest trying an acid drain cleaner -- your
problem may well be calcium.
The other folks are also right about longer snake, and perhaps the snake
going up instead of down.
At my local discount "dollar" store, they have bottles of drain cleaner
which are acid. Vinegar is a mild acid. And fairly cheap.
Christopher A. Young
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