Riddles, brain puzzles and mathematical problems

[Bridge]

I don't get it. The last rat still receives "512" bottles so it is impossible to find the poison in only 24 hours, wasn't that the point of the puzzle? You said it takes 10-20 hours for the poison to run its course and the scientist only has 24 hours to find the poison, implying that in a worst case scenario it must be done in one go (though it is possible to do it in two in if the poison decides to kill quickly.) Therefore, to satisfy the conditions of the puzzle it must be done in one go. With this method, ruling out 512 bottles is only the first step, you must then divide 512 bottles the same way, and then 256, then 128, etc … until you have only two. Therefore, way more than 24 hours and way more than 10 rats are required.