Re: Rec.Puzzles: Greatest Hits!
On Friday, March 22, 2013 at 1:32:58 AM UTC-7, mbuck wrote:
> A puzzle that has haunted me for about a decade from this group (which I cannot quite remember the details) involved two prisoners in adjacent cells who deeply distrusted each other, and a set of keys that they could reach if they worked together. The question was; how could they both ensure that they both got free? IIRC, we never figured out an optimal strategy...

----------------------- that sounds interesting.

a good puzzle i learned (read about) recently involves
two prisoners (A, B) and they each receive a card with an integer N (N>0) on it.

The two numbers are adjacent .... . . .

______________________________

Alice and Bob are on a game show. Each is secretly told a whole, positive number. They are told the two numbers are consecutive, but neither knows the other person’s number. For example, if Alice is told 20, she does not know if Bob was told 19 or 21. And if Bob is told 21, he does not know if Alice was told 20 or 22. The point of the game is to guess the other person’s number. The game works as follows.

–Alice and Bob cannot communicate with each other, and they are not allowed to plan their strategy either.

–The two are in a room where a clock rings every minute.

–After the clock rings, either player can call out a guess of the other player’s number, or they can stay silent.

–The game continues until Alice or Bob makes a guess. After the first guess is made, the game ends.

–Alice and Bob win $1 million each if the guess is correct, and they lose and get nothing if the guess is incorrect.

How should Alice and Bob play this game to have the best chance of winning? Each knows the other person is perfect at logical reasoning.

On 04/07/2022 19:06, henh...@gmail.com wrote:
>
>
> Re: Rec.Puzzles: Greatest Hits!
> On Friday, March 22, 2013 at 1:32:58 AM UTC-7, mbuck wrote:
>> A puzzle that has haunted me for about a decade from this group (which I cannot quite remember the details) involved two prisoners in adjacent cells who deeply distrusted each other, and a set of keys that they could reach if they worked together. The question was; how could they both ensure that they both got free? IIRC, we never figured out an optimal strategy...
>
>
> ----------------------- that sounds interesting.
>
>
>
>
> a good puzzle i learned (read about) recently involves
> two prisoners (A, B) and they each receive a card with an integer N (N>0) on it.
>
> The two numbers are adjacent .... . . .
>
>
> ______________________________
>
>
> Alice and Bob are on a game show. Each is secretly told a whole, positive number. They are told the two numbers are consecutive, but neither knows the other person’s number. For example, if Alice is told 20, she does not know if Bob was told 19 or 21. And if Bob is told 21, he does not know if Alice was told 20 or 22. The point of the game is to guess the other person’s number. The game works as follows.
>
> –Alice and Bob cannot communicate with each other, and they are not allowed to plan their strategy either.
>
> –The two are in a room where a clock rings every minute.
>
> –After the clock rings, either player can call out a guess of the other player’s number, or they can stay silent.
>
> –The game continues until Alice or Bob makes a guess. After the first guess is made, the game ends.
>
> –Alice and Bob win $1 million each if the guess is correct, and they lose and get nothing if the guess is incorrect.
>
> How should Alice and Bob play this game to have the best chance of winning? Each knows the other person is perfect at logical reasoning.
>

A player given number n should call that the other player has n+1 at
minute n. If the other player had n-1 they would have already called
out, the go before.