You can post that PM of mine if you want. Or I could post it. Or you could change the story I told you into another philosophy question dealing with something like spirits tryiing to get their temple work done so they can go to heaven or something.
It was a fun problem although it only took me about 10 min, and most of that was spent trying to figure out what the question was in the first place.
Anti-Mormons in the pre-existence (another problem)
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_asbestosman
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_Gadianton
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here is the answer i typed up the day I wrote it. I avoided math generalizations and explain it bit by bit from the perspective of being one of them.
a) If there is just one (with a mark), the revelation implies that because he cannot see the mark on any others, it must be himself who is marked. The next day, he leaves.
b) If there are two (with a mark), they each know the other has the mark but not themself. When the announcement comes, they each reason that in the case that they do NOT have the mark (remember, they don't know if they have it or not), that the other will make the correct deduction from a), and leave the next day. The next day comes, but because each sees the other with the mark still hanging around, each of them know another spirit must be marked, and since it doesn't see any others with the mark, each of them correctly deduce they are marked and they both leave together, the next day (the 2nd day after the anouncement).
c) If there are three (with a mark), they all know the other two are marked but not themselves. When the announcement comes, they have to do some seriously abstract thinking because they already know that not only is there one with a mark, but if they themselves didn't have a mark, then this would not be enough information for either of the other two marked spirits to make the a) deduction because those other two can see each other's mark and so the announcement wouldn't have told them what it did in b). But each of those three can reason like this: Let's say I'm not marked. Then the game is between the other two. If the game is between the other two, then each of those other two could reason that they are not marked! They can reason independently that if they are not marked, then this announcement will be new information for the one who would be alone in heaven with the mark. In other words, each of the three marked ones can reason that if they are NOT marked, then the other two will reason according to b), and they will be dead in two days. And so when his test hypothesis fails, and two days later the other two marked spirits still walk about heaven, they each respectively know there must be a third, and since they see no others, they out themselves and so on the third day, they all three together take a hike.
After grasping c), you can reiterate up to the 1000 as specified and see that it will be 1000 days. (you can make the general inference from b easily and guess right, but without fully understanding why)
a) If there is just one (with a mark), the revelation implies that because he cannot see the mark on any others, it must be himself who is marked. The next day, he leaves.
b) If there are two (with a mark), they each know the other has the mark but not themself. When the announcement comes, they each reason that in the case that they do NOT have the mark (remember, they don't know if they have it or not), that the other will make the correct deduction from a), and leave the next day. The next day comes, but because each sees the other with the mark still hanging around, each of them know another spirit must be marked, and since it doesn't see any others with the mark, each of them correctly deduce they are marked and they both leave together, the next day (the 2nd day after the anouncement).
c) If there are three (with a mark), they all know the other two are marked but not themselves. When the announcement comes, they have to do some seriously abstract thinking because they already know that not only is there one with a mark, but if they themselves didn't have a mark, then this would not be enough information for either of the other two marked spirits to make the a) deduction because those other two can see each other's mark and so the announcement wouldn't have told them what it did in b). But each of those three can reason like this: Let's say I'm not marked. Then the game is between the other two. If the game is between the other two, then each of those other two could reason that they are not marked! They can reason independently that if they are not marked, then this announcement will be new information for the one who would be alone in heaven with the mark. In other words, each of the three marked ones can reason that if they are NOT marked, then the other two will reason according to b), and they will be dead in two days. And so when his test hypothesis fails, and two days later the other two marked spirits still walk about heaven, they each respectively know there must be a third, and since they see no others, they out themselves and so on the third day, they all three together take a hike.
After grasping c), you can reiterate up to the 1000 as specified and see that it will be 1000 days. (you can make the general inference from b easily and guess right, but without fully understanding why)
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_Gadianton
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I heard a similar problem about prisoners with numbers on their foreheads. They cannot communicate with each other, and there are no mirrors. All prisoners can get free if one can guess the number on their own forehead. The possible numbers are 1 through N where N is the number of prisoners. Numbers can be doubled up. If I recall correctly, the solution is to have the prisoners stand in a line and count off. Add their order number to the sum of everyone else's number, then divide by N and take the remainder. If the remainder is 0, then choose N instead. It works because the prisoners are effectively guessing the sum of the N numbers (N-1 of which they know) modulus N which will be a number from 0 to N-1.
Your problem seems substantially different, but the solution might be the following. If anti-mormons are smart, they will realize that they can come to learn of who has the mark by keeping track of how many A's they see, and then leaving on that day + 1 unless everyone has already left. They woud realize they were the person on day N-1 because nobody would have left. They would then leave the next day. The ones without the A would realize on day N that they were not the ones because everyone else already left. The anti-mormons would be able to do this because they would know that the others have deduced the same thing--what with them being so clever and all.
Was I close?
the asb pm
Your problem seems substantially different, but the solution might be the following. If anti-mormons are smart, they will realize that they can come to learn of who has the mark by keeping track of how many A's they see, and then leaving on that day + 1 unless everyone has already left. They woud realize they were the person on day N-1 because nobody would have left. They would then leave the next day. The ones without the A would realize on day N that they were not the ones because everyone else already left. The anti-mormons would be able to do this because they would know that the others have deduced the same thing--what with them being so clever and all.
Was I close?
the asb pm
The interesting "side effect" of the problem:
If Heavenly Father writes that Scripture, reveals the excommunicative command, but actually doesn't use any mark, then - according to the logic used - everybody leave at the first day, and become an "A", unwillingly.
In the original "story" about mark on the foreheads, the true ones are marked:
Rev. 14: 1
And I looked, and, lo, a Lamb stood on the mount Sion, and with him an hundred forty and four thousand, having his Father’s name written in their foreheads.
If Heavenly Father writes that Scripture, reveals the excommunicative command, but actually doesn't use any mark, then - according to the logic used - everybody leave at the first day, and become an "A", unwillingly.
In the original "story" about mark on the foreheads, the true ones are marked:
Rev. 14: 1
And I looked, and, lo, a Lamb stood on the mount Sion, and with him an hundred forty and four thousand, having his Father’s name written in their foreheads.