Riddles, brain puzzles and mathematical problems

[BAndrew]

Done

[Froge]

Btw, uftmnes was not a solution to anything.

[MyRedNeptune]

@MyRedNeptune
Congratulations! You got it!



Do you want to post a problem? Let me know, because I have something in mind

Nah, go ahead. I don't have anything at the moment.

[BAndrew]

Btw, uftmnes was not a solution to anything.

I know
I just use it for fun.

Nah, go ahead. I don't have anything at the moment.

OK then.

A mad scientist has 1000 bottles of a new medicine, but one of them is poisoned. The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison. In just under 24 hours the king and the rest of the citizens, who are ill, are going to try the medicine. Therefore he must find the poisoned bottle and remove it until then. He has 1000 rats at his disposal which can be used to test the bottles (unfortunately this will probably result in their death if they drink the poison). What is the minimum ammount of rats required in order for the mad scientist to make it on time?

[Bridge]

Spoiler below!

The scientist must uncover the poison within 24 hours so the absolute minimum speed at which he can administer the medicine to the rats and still meet the deadline is ~42 bottles per hour (1000 bottles/24 hours). Since it takes 10-20 hours for the poison to kill that means the minimum amount of bottles lies somewhere between ~417 and ~833 bottles (~42 * 10 and ~42 * 20 respectively) and therefore just as many rats are required. This of course assumes he has time to check whether any rats have died after 10-20 hours while still continuing to check the bottles.

My best guess.

[BAndrew]

@Bridge

Unfortunately your answer is incorrect. If he follows your method then he won't know which bottle is poisoned because there is not a "1-1" correspondence (rat-bottle).

[Bridge]

Not if he devises a cataloging system, which my answer assumed.

[BAndrew]

Not if he devises a cataloging system, which my answer assumed.

Then I haven't understood it properly. How will he do it?

[Bridge]

Numbers the bottles and rats, so that each bottle has a number corresponding to a rat and vice versa. Is that not allowed?

[BAndrew]

Yes it is. So you are saying for instance:

Rat 1 --> Bottle 1
Rat 2 --> Bottle 2
.
.
.
Rat 1000-->Bottle 1000

So if rat NO.666 dies then it means that the 666th bottle is poisoned. Is that what you meant?