The mice problem 
Problem. You have $2$ mice, and $9$ bottles, exactly one of which is poisoned. Each mouse can taste any combination of bottles at once, and if it is poisoned it will die after exactly one minute. Once a mouse is dead, it can't taste any more bottles. How many minutes do you need to determine exactly which bottle is poisoned?
This question has me in a complete bind. Anyone who can point me in the right direction as to how to get started with this problem would be greatly appreciated.
 A: Here is how you could approach it(fill in the blanks):
In the first minute, give mouse A bottles $1$, $2$, and $3$. Give mouse B $3$, $4$, and $5$.
If both of them die, what does that mean for a bottle of $3$?
If only A dies, give B a bottle of $1$ in the second minute and see what happens.
Likewise, if only B dies give A bottle $4$ and see what happens.
If none die, give B bottles $6$ and $7$ and give A $7$ and $8$ in minute two, proceeding like above.
If none of them die, there is only one bottle remaining.
Hope this helps.
EDIT: This takes max $2$ minutes in total.
A: (Note: This answer isn't the best one since it ignores one of the pieces of information, both mice die.)
At step one, mouse 1 tastes 1,2,3 combined; mouse 2 tastes 4,5,6 combined; if both survive mouse 1 tastes bottle 7, mouse 2 bottle 8, with an answer in 2 minutes.
If mouse 1 dies after step one, mouse 2 then tastes bottle 2, then if it survives bottle 3, with an answer in 2 (1 case) or 3 (2 cases) minutes. Similarly, if 2 dies after step one, mouse 1 tastes 4 then 5.
So you need average of $ (2\times 3+2\times 2+3\times 4)/9=2\frac49 $ minutes.
This problem is an information theoretic problem similar to Huffman encoding with an alphabet of four signals, the signals being "mouse 1 dies", "mouse 2 dies", "both mice die", and "nobody dies". The above solution ignored the case of "both mice die".
A: This is one of those trick interview questions where the idea is to see if you can think quickly enough on your feet to realise the problem is trivial. The key is to realise that you do not have to wait for the results of one test to start another one.
So you give the first dose to a mouse at t=0, the second at t+ε,...,t+7ε and check carefully the time at which it dies. Note that the question specifies that the mouse dies after exactly one minute.
So the answer is 'a little over 1 minute, for some definition of a little'.
[Answer as noted in a comment by @ConnorGordon].
