Riddles, brain puzzles and mathematical problems

[BAndrew]

@BAndrew (what's up with the new name? ) - Hm, I'm having trouble understanding your solution. Which rats get which medicine? I'm a bit confused.

Actually he didn't meant to do this.

Also, part of this sentence is incorrect. Can you guess which?

It doesn't matter which rats get which medicine (you do it however you want) as long as there is a "1-1" correspondence.
Every combination of rats corresponds to a bottle. (eg rat 1 + rat 2 + rat 5 corresponds to bottle 431 you decide how (it doesn't matter)). There are 1024>1000 possible combinations therefore after 20 hours you can check which rats died and then see which bottle they correspond to.

More mathematically defined:
a x combination of rats corresponds to a y bottle

A={1,1-2,1-2-3,1-5,5-7...}set of all combinations of rats
B={1,2,3,4,...1000} set of bottles

f:A-->B where f(x) = y
f is "1-1" which means that a x combination of rats corresponds to exactly one bottle and vice versa.




PS. wow I used didn't + meant in the same sentence. My grammar is perfect!