• #### names in boxes

From duncan smith@21:1/5 to All on Thu Feb 29 00:54:40 2024
Hello,
I've come across a problem (puzzle) in some Cambridge University (statistics) notes that I don't remember being posted here. So I thought
it might be of interest.

The names of 100 prisoners are placed in 100 boxes (one name in each
box) which are lined up on a table in a room in an order unknown to the prisoners. Each prisoner must enter the room and is allowed to look in
up to 50 boxes to try to find their name. If any prisoner fails to find
their own name, the they are all executed.

Each prisoner must leave the room in the exact state they found it when
they entered. No communication is allowed between any prisoners once the procedure has started. The prisoners are allowed to meet to devise a
strategy before the process starts. Find a strategy that gives the
prisoners a probability of survival of greater than 0.3.

Cheers.

Duncan

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• From G@21:1/5 to duncan smith on Thu Feb 29 09:33:07 2024
duncan smith <duncan@invalid.invalid> wrote:
Hello,
I've come across a problem (puzzle) in some Cambridge University (statistics) notes that I don't remember being posted here. So I thought
it might be of interest.

The names of 100 prisoners are placed in 100 boxes (one name in each
box) which are lined up on a table in a room in an order unknown to the prisoners. Each prisoner must enter the room and is allowed to look in
up to 50 boxes to try to find their name. If any prisoner fails to find
their own name, the they are all executed.

Each prisoner must leave the room in the exact state they found it when
they entered. No communication is allowed between any prisoners once the procedure has started. The prisoners are allowed to meet to devise a
strategy before the process starts. Find a strategy that gives the
prisoners a probability of survival of greater than 0.3.

Cheers.

Duncan

I have seen this before, but I don't think this version is solvable as it has no way to connect a name with a box. The (solvable) version I know has the prisoner NUMBERS (from 1 to 100) randomly placed in the numbered boxes.

G

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• From Mike Terry@21:1/5 to All on Thu Feb 29 16:42:33 2024
On 29/02/2024 09:33, G wrote:
duncan smith <duncan@invalid.invalid> wrote:
Hello,
I've come across a problem (puzzle) in some Cambridge University
(statistics) notes that I don't remember being posted here. So I thought
it might be of interest.

The names of 100 prisoners are placed in 100 boxes (one name in each
box) which are lined up on a table in a room in an order unknown to the
prisoners. Each prisoner must enter the room and is allowed to look in
up to 50 boxes to try to find their name. If any prisoner fails to find
their own name, the they are all executed.

Each prisoner must leave the room in the exact state they found it when
they entered. No communication is allowed between any prisoners once the
procedure has started. The prisoners are allowed to meet to devise a
strategy before the process starts. Find a strategy that gives the
prisoners a probability of survival of greater than 0.3.

Cheers.

Duncan

I have seen this before, but I don't think this version is solvable as it has no way to connect a name with a box. The (solvable) version I know has the prisoner NUMBERS (from 1 to 100) randomly placed in the numbered boxes.

G

Right - the prisoners would have to assign numbers 1-100 to themselves and remember that
association! Or maybe they can all write the list down and take the list into the room with them...

Mike.

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• From duncan smith@21:1/5 to Mike Terry on Fri Mar 1 01:22:49 2024
On 29/02/2024 16:42, Mike Terry wrote:
On 29/02/2024 09:33, G wrote:
duncan smith <duncan@invalid.invalid> wrote:
Hello,
I've come across a problem (puzzle) in some Cambridge University
(statistics) notes that I don't remember being posted here. So I thought >>> it might be of interest.

The names of 100 prisoners are placed in 100 boxes (one name in each
box) which are lined up on a table in a room in an order unknown to the
prisoners. Each prisoner must enter the room and is allowed to look in
up to 50 boxes to try to find their name. If any prisoner fails to find
their own name, the they are all executed.

Each prisoner must leave the room in the exact state they found it when
they entered. No communication is allowed between any prisoners once the >>> procedure has started. The prisoners are allowed to meet to devise a
strategy before the process starts. Find a strategy that gives the
prisoners a probability of survival of greater than 0.3.

Cheers.

Duncan

I have seen this before, but I don't think this version is solvable as
it has
no way to connect a name with a box. The (solvable) version I know has
the
prisoner NUMBERS (from 1 to 100) randomly placed in the numbered boxes.

G

Right - the prisoners would have to assign numbers 1-100 to themselves
and remember that association!  Or maybe they can all write the list
down and take the list into the room with them...

Mike.

Exactly. I assume the prisoners should allocate numbers to themselves
randomly to guarantee the 0.3 probability of survival, as the problem
doesn't specify that the boxes are ordered randomly.

Duncan

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