Riddles, brain puzzles and mathematical problems

[Bridge]

Yep, exactly.

[BAndrew]

Yep, exactly.

OK then but with this method he is going to use all of the 1000 rats. You have to find the minimum number of rats required in order to be sure that the bottle X is poisoned. In other words you have to make the method more elegant.

[Bridge]

Spoiler below!

I just noticed that my method contains some errors so ignore it. If you think about it though, the absolute minimum amount of rats he needs for him to be sure that he discovers the poison is all of them. The worst case scenario is always going to be that the last bottle he checks is the one that contains the poison, right?

[BAndrew]

Spoiler below!

I just noticed that my method contains some errors so ignore it. If you think about it though, the absolute minimum amount of rats he needs for him to be sure that he discovers the poison is all of them. The worst case scenario is always going to be that the last bottle he checks is the one that contains the poison, right?

It seems that way, but I promise there is an ingenious way where he can do it with MUCH less rats that you think. Try to think outside the box. I suggest you deal first with smaller numbers (eg 10 bottles)

[Bridge]

Spoiler below!

I just noticed that my method contains some errors so ignore it. If you think about it though, the absolute minimum amount of rats he needs for him to be sure that he discovers the poison is all of them. The worst case scenario is always going to be that the last bottle he checks is the one that contains the poison, right?

It seems that way, but I promise there is an ingenious way where he can do it with MUCH less rats that you think. Try to think outside the box. I suggest you deal first with smaller numbers (eg 10 bottles)

Spoiler below!

I considered that exact concept, of administering 10 bottles to each rat, but there isn't enough time for it to be feasible.

I might think over the problem tomorrow, if you say it can be solved.

[BAndrew]

OK not need to hurry, take your time.

Even if you could administer 10 bottles to a single rat then you would have a problem because if the rat dies then you can't know which of these 10 bottles is the one with the poison

[MyRedNeptune]

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?

Can I split one bottle into several (please)?

[BAndrew]

Nope. But even if you could I can't see how this helps you.

[Bridge]

OK not need to hurry, take your time.

Even if you could administer 10 bottles to a single rat then you would have a problem because if the rat dies then you can't know which of these 10 bottles is the one with the poison

Spoiler below!

I know. You do 100 tests, and if any of the rats die you repeat the process taking away one bottle each time. Highly impractical and of course not possible in this situation, but it saves 891 rats.

[MyRedNeptune]

Nope. But even if you could I can't see how this helps you.

Dammit. Well ok. It actually doesn't matter anyway.

Spoiler below!

The answer is 10 rats.

Let's arrange our medicine into a row of 1000 bottles plus 24 imaginary bottles. It is possible to find the poison in 10 steps. Each step 1 rat will be used.

1. Split the row of 1024 in halves A and B and give A (512 samples of medicine) to rat 1.
2. Split A and B into AA, AB, BA, BB and give AA and BA to rat 2.
3. Split AA, AB, BA, BB into AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB and give AAA, ABA, BAA, BBA to rat 3.

Continue in such a manner to step 10, where rat 10 will be given all the odd-numbered samples. Each step the rat will either die or stay alive, limiting the possible area of location of the poison by half.

This chart, in which each separate rat's sample portion is marked by a darker cell color, illustrates the proccess:

P.S. Sorry it took so long. I had it ready after my last post but I made a bit of a detour.