Thinset on paint OK?

I just finished basement drywalling and painting. I used spray paint and didn't mask the concrete floor. As a result, I have a lot of primer/paint on the floor, particularly around perimeter of each room.
Now I am going to lay cemeric tiles (over 1000 of 12"x12" tiles) using thinset. I was wondering if it is OK with minimum cleaning of paint on the floor when tiling? I tried to wash the floor with a hose, and the paint around perimeter just won't come off. I poured some paint remover. But the spill over the new wall.
Thanks for the advice.
Y.
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I just had this done by a professional, and he spent more than a day removing old paint. He didn't remove every bit of paint, but most of it was gone before the tiles were put on. It was the hardest part of the job, but evidently necessary. If you mess that up, you may later end up with loose tiles and broken tiles that might be hard to replace. I would spend the time and do it properly.
Dave

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I have found that a sand blaster is very useful for removing paint from concrete.
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A trip with a good floor scraper should suffice. Use fresh sharp blades.
Here is one brand:
http://www.craintools.com/fs-tear-outtools.html
look at #350 or 360 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Keep the whole world singing . . . . DanG (remove the sevens) snipped-for-privacy@7cox.net

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I posed this question to the tile guy at the local Home Depot store and he recommended me to use "Armstrong S-184 Fast-Setting Patch & Skim Coat".
Although I bought the product, I have not used it yet.
Lewis. (the worlds slowest tile guy)
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