Mice and Wine

This is one of my favorite problems:

You’re planning a huge party for tomorrow, which will include a toast exactly 24 hours from this moment.  You have 1000 bottles of wine, but one of them is contaminated with a slow-acting poison that will kill any living thing within 24 hours of being ingested.  You happen to have 10 altruistic mice on hand who have volunteered to test the poison.  How many bottles of wine can you safely serve at the toast?

I’ve given it to a number of classes, ranging in age and strength, and it’s produced wonderful discussions every time.  Here’s a reconstruction of how many of these have gone.

Right off, several students come up with the idea of splitting up the 1000 bottles evenly among the 10 mice.  When one of the mice dies, they explain, you would know that the poisoned bottle was among the 100 that it drank, and so the remaining 900 would be safe to serve.