Rat Problem

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Since there are 1000 bottles and 10 rats, I thought to split the work evenly at the start. Each rat drinks 100 bottles. This means that 1 of the rats will die, which means that the poisoned bottle will be in that 100 set of bottles the rat was assigned. So now we have 9 rats left to test 100 bottles. Now set 1 bottle aside and have the rats test 99 of the bottles. Each of the 9 rats will test 11 bottles each. If no rats die, then we somehow amazingly picked out the poisoned bottle. But most likely one of the rats will die, and we will know that in their group of 11 bottles there will be one that is poisoned. So now we have 8 rats remaining to test 11 bottles. Set 3 bottles aside so that we have 8 bottles and 8 rats. Each rat will drink one, if they all live then the poisoned bottle is in the group of 3, if not then whichever bottle the dead rat drank from is poisoned. If they all live then we have 8 rats to test 3 bottles, which is trivial. Let 3 rats each drink a bottle, whoever dies drank from the poisoned one. Worst case scenario will have us losing 4 rats to find the poisoned bottle, which I would definitely take over poisoning my guests. I think there is a more optimal trick to find the poisoned bottle, but I'm not too sure. I believe there are many different answers to this problem, which is a good chance for students to be creative!

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