Online Communication Solutions

Prisoners Brain Teaser?

100 prisoners are trapped on an island. They are each assigned a number 1 to 100. The warden tells them they must all complete the following task. If a single one of them fails they all will be executed. If all are successful they are released. They will each go in to a room where 100 cards (numbered 1 to 100) are placed in a random order face down on a table. They are permitted to turn over 50 of the cards and their task is to turn over their number. Once they do this the cards are returned to their original positions and the next prisoner tries to do the same. No communication is allowed between the prisoners. However, they may come up with a preset strategy. What should they do?

each prisoner turns their own number-position as “first card turned” and follows the number appeared on the card (as a number-position) to turn a second card and so on.

example :
prisoner #1 turns over the card at (1,1) position [assuming the cards are arrange in 10x10 coordination]. whatever number (s)he gets, N = 10x + y, the prisoner change it into a coordinate of (x+1, y). let’s say the (1,1) card is numbered 27, so the 2nd card he turn will be (3,7). he keeps doing so until he find his own number or he had already turned 50 cards in all, whichever comes first.

“The probability that a permutation does not have cycles with length larger than 50 is

P = 1- 1/51 – 1/52 – … – 1/100 = 0.311828″ — by Zo Maar-san.

basically, they just turn the cardinal numbers into ordinal numbers (associating with any order of arrangement there is) and do it up to 50 times.

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