Skip to main content
Puzzling

Return to Question

Post Made Community Wiki by user20
added 30 characters in body
Source Link
user88
user88

Since there have been quite a few poisoned-bottle problems posted to the site already, I thought I'd post a general formula to cover all future variations of this problem (at least where a single poisoned bottle is concerned).

You have $n \le (m+1)^k$ bottles of wine, one of which is poisoned. You have $m$ days to conduct death trials, and $k$ prisoners to test the wine with. The poisoned wine kills any person who drinks it at the stroke of midnight on the day that they drank it. You have $k$ prisoners to test the wine by making them drink it and possibly killing them, and $m$ days to conduct these death trials. How do you plan out the tests so that you can figure out which bottle is poisoned?

Since there have been quite a few poisoned-bottle problems posted to the site already, I thought I'd post a general formula to cover all future variations of this problem (at least where a single poisoned bottle is concerned).

You have $n \le (m+1)^k$ bottles of wine, one of which is poisoned. You have $m$ days to conduct death trials, and $k$ prisoners to test the wine with. The poisoned wine kills any person who drinks it at the stroke of midnight on the day that they drank it. How do you plan out the tests so that you can figure out which bottle is poisoned?

Since there have been quite a few poisoned-bottle problems posted to the site already, I thought I'd post a general formula to cover all future variations of this problem (at least where a single poisoned bottle is concerned).

You have $n \le (m+1)^k$ bottles of wine, one of which is poisoned. The poisoned wine kills any person who drinks it at the stroke of midnight on the day that they drank it. You have $k$ prisoners to test the wine by making them drink it and possibly killing them, and $m$ days to conduct these death trials. How do you plan out the tests so that you can figure out which bottle is poisoned?

Post Undeleted by user88
Post Deleted by user88
Source Link
user88
user88

The completely generalized poisoned-bottle problem

Since there have been quite a few poisoned-bottle problems posted to the site already, I thought I'd post a general formula to cover all future variations of this problem (at least where a single poisoned bottle is concerned).

You have $n \le (m+1)^k$ bottles of wine, one of which is poisoned. You have $m$ days to conduct death trials, and $k$ prisoners to test the wine with. The poisoned wine kills any person who drinks it at the stroke of midnight on the day that they drank it. How do you plan out the tests so that you can figure out which bottle is poisoned?