Comments by "Игоррь Романов" (@igorrromanov) on "Разгадка, в которую невозможно поверить: задача о 100 заключённых [Veritasium]" video.

  1. In this problem there is one grain of gold that implies with 100% certainty that the prison authorities are not in the pursuit to make this problem unsolvable. It is said: if but A SINGLE prisoner will miss his number, then ALL prisoners are to be executed. Imagine now that the very first prisoner misses his number because the chain is sadistically made of 100 elements (i.e. a SINGLE chain). The very first one with bulletproof certainty misses his number - AND IN THAT VERY MOMENT THE ASSIGNMENT COMES TO AN ABRUPT END. Which means that from the very beginning the concept of this assignment was a pure absurdity. Therefore we can make a healthy assumption that there are either: 1) 2 chains with equal number if elements (which is the most likely arrangement) or: 2) Several chains with different number of elements, either almost equal (the least likely arrangement) or made of quite variable number of elements (with the likelihood somewhere in between two previously described arrangements). Therefore, in practice no chain contains more than 50 elements.
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  2. Here is the TRULY sadistic approach (ATTENTION: Prison authorities INTENTIONALLY make this problem 100% solvable): Any prisoner (with everyone of them finding his number!) HAS TO MARK one box in his chain at his discretion. The number of the checked box plus the number contained in the box make the number of a certain prisoner (if the resulting number is more than 100% than to subtract 100 from the resulting number). Make any chain of no less than 8 elements. Whoever will receive 3 strikes will be hanged by an old method (i.e. without dropping trapdoor). Whoever will receive 4 strikes will be broken on the wheel. Whoever will receive 5 or more strikes will be burned at the stake on slow fire. I think that this endgame is the only one which will make all the prisoners miserable indeed.
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