Marx and Engels
The head of the concentration camp summons 5 convicts and says:
“You will have time until the evening to create an action plan, but tomorrow you will be in different cells and will never meet. We have a Lenin's room in the camp, in which there are 2 books on the table: Marx's Capital and Engels's Anti-Dühring.
Starting next week, I will choose one of you and take him to the Lenin's room for political information. There is no need to read anything, but it will be necessary to take any (but only one) of the books and turn it over (from the back to the cover or vice versa). Except you, no one will go to the Lenin's room. I will choose the prisoners as I want: for example, today I bring together the first three times, and tomorrow we will take everyone in turn, and the day after tomorrow you will manage.
')
Sooner or later each of you will visit the Lenin's room. So, any of you at any time can say "We have all been here already!". If he turns out to be right, you will all be released. If not, they are shot. ”
What to do convicted, because the time until the evening is still there?
UPD: Make it easy. The prisoners are not 5, but 19.
UPD: The answer is quite quickly and clearly formulated by fellow tunelix , based on the almost correct version by FloppyFormator :
So: we have 1 counter and 4 performers.
the task of the performer: if Marx is the cover of the top - we turn Engels over, if the cover down we turn Marx upside down. each artist considers the number of Marx’s revolutions - if he turned him over 2 times - the more he doesn’t turn him upside down.
counter: every time when he sees Marx turned upside down he increases the counter +1 and turns Marx down with his face. if Marx is lying face down, he cyclically turns Engels over.
when the counter reaches 8 - he can say that everyone has been in the room.
counting up to 8 (and not up to 4x) is necessary to bypass the situation when the meter enters the room, and there the Marx lies face up.
A few thoughts about the task and its discussion:
1. In the original (when I found out about it) the task was about 2 switches and 23 prisoners. I had to redo the patriotic style, so that the public is not so quickly googled the answer.
2. The task was intentionally complicated. So, for example, 5 prisoners together with 2 books suggest thoughts about the binary number system, although you don’t even think with 23 prisoners in this (wrong) direction. In addition, if you reduce the task to one book (by removing a prerequisite for a coup of at least one book), then the problem is also solved much easier. But finding the right direction is also a task, so you shouldn’t make claims about incorrect wording.
3. The condition that each prisoner will visit the room several (yes, there are many!) Was not explicitly stated, because if this were not the case, the task would obviously not have a solution.
4. The search for 'alternative' options (turning books around the axis, making notes, bookmarks, putting Marx under the handle with Engels, etc.) was far from reasonable. The conditions of the problem are quite enough to solve it.
5. Not everyone understood what was required of them. For me, the right decision satisfies the following conditions: a) prisoners will not be shot under any circumstances; b) prisoners have a real chance to get out. Even with these fairly general criteria, only one solution was found.
“You will have time until the evening to create an action plan, but tomorrow you will be in different cells and will never meet. We have a Lenin's room in the camp, in which there are 2 books on the table: Marx's Capital and Engels's Anti-Dühring.
Starting next week, I will choose one of you and take him to the Lenin's room for political information. There is no need to read anything, but it will be necessary to take any (but only one) of the books and turn it over (from the back to the cover or vice versa). Except you, no one will go to the Lenin's room. I will choose the prisoners as I want: for example, today I bring together the first three times, and tomorrow we will take everyone in turn, and the day after tomorrow you will manage.
')
Sooner or later each of you will visit the Lenin's room. So, any of you at any time can say "We have all been here already!". If he turns out to be right, you will all be released. If not, they are shot. ”
What to do convicted, because the time until the evening is still there?
UPD: Make it easy. The prisoners are not 5, but 19.
UPD: The answer is quite quickly and clearly formulated by fellow tunelix , based on the almost correct version by FloppyFormator :
So: we have 1 counter and 4 performers.
the task of the performer: if Marx is the cover of the top - we turn Engels over, if the cover down we turn Marx upside down. each artist considers the number of Marx’s revolutions - if he turned him over 2 times - the more he doesn’t turn him upside down.
counter: every time when he sees Marx turned upside down he increases the counter +1 and turns Marx down with his face. if Marx is lying face down, he cyclically turns Engels over.
when the counter reaches 8 - he can say that everyone has been in the room.
counting up to 8 (and not up to 4x) is necessary to bypass the situation when the meter enters the room, and there the Marx lies face up.
A few thoughts about the task and its discussion:
1. In the original (when I found out about it) the task was about 2 switches and 23 prisoners. I had to redo the patriotic style, so that the public is not so quickly googled the answer.
2. The task was intentionally complicated. So, for example, 5 prisoners together with 2 books suggest thoughts about the binary number system, although you don’t even think with 23 prisoners in this (wrong) direction. In addition, if you reduce the task to one book (by removing a prerequisite for a coup of at least one book), then the problem is also solved much easier. But finding the right direction is also a task, so you shouldn’t make claims about incorrect wording.
3. The condition that each prisoner will visit the room several (yes, there are many!) Was not explicitly stated, because if this were not the case, the task would obviously not have a solution.
4. The search for 'alternative' options (turning books around the axis, making notes, bookmarks, putting Marx under the handle with Engels, etc.) was far from reasonable. The conditions of the problem are quite enough to solve it.
5. Not everyone understood what was required of them. For me, the right decision satisfies the following conditions: a) prisoners will not be shot under any circumstances; b) prisoners have a real chance to get out. Even with these fairly general criteria, only one solution was found.
Source: https://habr.com/ru/post/25820/
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