5 ms·
on the mouse one, could you not mix wines? 100 bottles, divide into 2 groups, feed mouse... Separate poisoned bottles into 2 groups feed mouse.. basically 10
by redorb 19y ago
on the mouse one, could you not mix wines?
100 bottles, divide into 2 groups, feed mouse...
Separate poisoned bottles into 2 groups feed mouse..
basically 100,50,25,12,6,3,1 ... 6 mice needed.
- martianpenguin 19y agoThere is only 1 day. Wouldn't you just separate the bottles evenly across all the mice?
- paulgb 19y agoThat way you could serve 900 bottles. Can you serve more? Hint: Look at the number of possible outcomes. In this case, each of the 10 mice can either live or die. That gives us 2^10 = 1024 possible outcomes. We can only encounter 1000 possible initial configurations of bottles. Is there a way to set it up so that each of the 1000 possible outcomes maps to an initial configuration?
- colonhyphenp 19y agoI figured it out by thinking what would happen if you only had 1 mouse (500 bottles can make it to the party), then looking at the problem again with 2 mice (there's a way to prove that 750 bottles are poison-free using only 2 mice), etc. all the way up to 10 mice.