[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 336

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MetaDriver писал(а) >>

And yet it doesn't guarantee it. What if Stirlitz is only taken to see a lamp three times?

Quote: And don't worry about anyone being forgotten - if you keep quiet, you'll all be in the room, and no visit to the room will be the last one for anyone.
 
If someone kept silent (only Stirlitz can tell, according to the agreement of the prisoners themselves), then everyone will have been in the cell at least once.

Here's proof (not mine, but read out) of the option where Stirlitz turns it off:
Indeed, every prisoner except the "meter" will not turn on the light in the room more than once. When the "meter" counts 99, he can be sure that all the other prisoners have been in the room at least once, except he himself has already been in the room. This means that at this point, all the prisoners will have been in the room at least once.

Остаётся доказать, что каждый из 99 узников включит свет. Предположим, что это не так - свет будет включён менее 99 раз. Тогда, начиная с некоторого дня n, свет включаться не будет. Так как никакой заход в комнату не будет для счётчика последним, он побывает в комнате после этого дня (например, на m-й день, m>n). Если свет при этом горел, он его выключит. Значит, начиная с (m+1)-го дня свет будет всё время выключен. Рассмотрим узника, который свет ещё ни разу не зажигал. Так как и для него никакой заход в комнату не последний, он побывает в комнате после m-го дня. Но тогда он должен включить свет - противоречие.

 
The five numbers was just a warm-up, so that the kids wouldn't think they were fools. These simple ones can be found at any Olympiad.
 
MetaDriver >>:

// Остался вопрос - нет ли более короткого решения. К тому же Штирлица могут и 55 раз привести, а потом не пущать.

Well, that's the most important thing.

loop to infinity
 
Well, that's for the warden to decide :) The important thing is that he ensures that everyone is sure to visit at least once - until Stirlitz confesses.
 
so where's the solver?
 
Stirlitz. He's in charge and counts everything.
 
Mathemat >>:
Штирлиц. Он главный и все считает.

So who's in charge? The probation worker or Stirlitz?

Who's in charge?

 
Mathemat >>:
Штирлиц. Он главный и все считает.

By then either the Stirlitz will be dead or the warden or one of the "non-experts" will have died. We'll have to rot in jail after all.

 
Stirlitz woke up in a prison cell.

He had no recollection of how he got here, what day it was, or what authority there was in the city. After much deliberation, he finally decided that if a Gestapo man entered, he should say: "Heil Hitler, I am Standartenfuhrer SS von Stirlitz", and if a Soviet soldier entered, he should introduce himself: "I am Colonel Isayev". At that moment a policeman comes in and says:

"You were drunk yesterday, comrade Tikhonov."
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