Reply to Re: Two interesting puzzles
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I don't think you meant "simultaneously" in the last puzzle... It means "at the same time". If two things happen simultaneously, then they happen at the same time.
If you meant that every prisoner can be chosen a max of 3 times during the whole process, it's easy (using the pidgeon hole principle).
If you mean that one prisoner can be chosen any amount of of times, as long as it's broken up in series of three, nothing will stop the warden from choosing (1,2,1,2,1,2,1,2,1,2,1,2... etc), so there's not always a solution.
So, assuming there's an all-time maximum of 3, and that really every day a prisoner will be chosen, then every prisoner has been chosen three times after 23*3 = 69 days. You can reduce this to 67 days once you realise the last two have to have gone before. This upper bound still holds when the prisoners can't count the days.
Now, finding the exact day on which the last prisoner finally goes to the room for the first time is a bit tricky, since that last person has to know he is the last. This is probably where the switches get into the picture.
Can the prisoners count the days?
If you meant that every prisoner can be chosen a max of 3 times during the whole process, it's easy (using the pidgeon hole principle).
If you mean that one prisoner can be chosen any amount of of times, as long as it's broken up in series of three, nothing will stop the warden from choosing (1,2,1,2,1,2,1,2,1,2,1,2... etc), so there's not always a solution.
So, assuming there's an all-time maximum of 3, and that really every day a prisoner will be chosen, then every prisoner has been chosen three times after 23*3 = 69 days. You can reduce this to 67 days once you realise the last two have to have gone before. This upper bound still holds when the prisoners can't count the days.
Now, finding the exact day on which the last prisoner finally goes to the room for the first time is a bit tricky, since that last person has to know he is the last. This is probably where the switches get into the picture.
Can the prisoners count the days?
